Christmas is the season of giving and Chelsea are proving particularly charitable when it comes to headlines right now.
The Premier League champions continue to struggle in the wrong half of the table and sacked manager Jose Mourinho last week.
The fallout from that continues with Chelsea also being linked with a number of new signings in the January transfer window.
The striker only arrived at Anfield in the summer, but injuries have played a part in his impact being less significant than many thought it would be.
Benteke had spent three seasons with Aston Villa where he made a real name for himself, scoring the goals that kept Paul Lambert's struggling side in the Premier League.
Since his departure, Villa's form has only got worse. Without the 25-year-old leading the line, they lack any presence up front, which is testament to just how vital he was.
Rather than being the ideal step up, joining Liverpool has stunted Benteke's development, though. The injuries haven't helped, while Liverpool's own change of manager has meant the forward has struggled to fit in under Jurgen Klopp.
So would he suffer the same fate if he moved to Stamford Bridge? Let's take a look at some of the key factors.
It's no surprise Benteke hasn't adjusted to life under Klopp at Anfield. Not because he isn't a striker of considerable talent, but more because his attributes aren't particularly suited to the way the manager likes his teams to play football.
Take Klopp's time at Borussia Dortmund, where he moulded Robert Lewandowski into a goal machine.
Lewandowski has continued to flourish since he moved to Bayern Munich as the systems Klopp and Pep Guardiola play aren't all that different.
Both managers preach the doctrine of the high press. They demand their players win the ball high up the pitch and turn teams quickly, putting them on the back foot.
Lewandowski is a mobile striker who fits into this system. He's very much a striker for the modern age in that regard, given how he can contribute to winning back possession and attacking players. He doesn't have to be resting on the shoulder of the last man.
Benteke is almost the antithesis of that. Much more physical, the Belgian is a target man who can bulldoze his way through defences and intimidate them.
He's skilful and better with the ball than he is maybe given credit for, but he isn't nimble in the same way as a player such as Lewandowski. He needs to develop that side of his game in order for Klopp to get the best out of him.
If he joined Chelsea, Benteke would slot almost seamlessly into the current setup. Ever since Didier Drogba's arrival over a decade ago, it's those target men that have thrived as Chelsea's strikers.
When Fernando Torres was signed in 2011 in an attempt to evolve the team's style, he failed. Even now, four years on, the need for a bulky, imposing front man is paramount for Chelsea.
It's no surprise that Benteke was on the list of Mourinho's January targets ahead of his sacking and interim boss Guus Hiddink is expected to maintain interest.
Compared with his last three seasons in English football, Benteke is just about par for this time of the year.
He has just four goals in the Premier League—his last coming over six weeks ago, coincidentally against Chelsea in Liverpool's 3-1 victory at Stamford Bridge.
At this stage in his debut campaign, he had scored eight times for Aston Villa, followed up with five in 2013/14 and just two last year.
It's post-Christmas that we've seen the best from him, mainly due to Benteke remaining fit and playing more consistently.
In that debut campaign, he scored six goals in five games from late January to mid-February and added a further eight before the season was out to finish with 23 in all competitions.
The following season he scored six times between January and March, when injury eventually ended his campaign prematurely.
In 2014/15, Benteke scored 14 goals after the Christmas period in a struggling Villa side that narrowly avoided the drop.
The pattern for the Belgian's form suggests he's a new man in the new year. Never is he as lethal in front of goal, which bodes well for Chelsea.
Any players Hiddink signs now must make an instant impact, and Benteke's form from January to May in the past few seasons suggests he will.
Benteke vs. Diego Costa/Loic Remy/Radamel Falcao
Would Benteke strengthen Chelsea's front line? That's the big question that must be answered as bringing him to Stamford Bridge will not come cheap.
Liverpool paid Aston Villa £32.5 million just six months ago, per BBC Sport. Despite the striker not making a massive impact, the Reds will not want to lose any of that initial investment.
Besides, every man and his dog knows Chelsea are desperate and Liverpool will want to hike up the price to ensure they're not allowing a rival to strengthen on the cheap. For that sort of money, Benteke will not be coming in to warm the bench.
Looking at how he impacts games and his physique, Benteke offers more than Loic Remy and Radamel Falcao at least.
It's pointless discussing the latter at length in the debate as the Colombian has been so ineffective. Falcao's loan move from Monaco has been a disaster.
Remy has been cut a raw deal, though. He has goals in him, but he hasn't been given a fair crack at the whip at Chelsea.
The main issue is that the former Queens Park Rangers man requires Chelsea to play a different way in order to get the best out of him, which this team doesn't seem capable of doing.
Chelsea need a straight swap for Diego Costa, which Benteke is close to being.
Both can play that lone-striker role expertly and aren't afraid of letting defenders know they are there. For Costa, that often means him running a fine line, although Benteke seems to revel more in the challenge than the scrap.
Both are accomplished finishers, as their past tallies show. For Costa, this calendar year—let alone the season—hasn't been productive enough, though. He's scored just 11 times in all competitions to Benteke's 19 in 2015.
The talent is there, but Costa hasn't been focused. With a player to challenge him like Benteke would, it could produce the sort of rivalry that drives every successful team.