The Daily Telegraph's Matt Law has certainly kept tabs on the story. In March he described Lukaku as "one of their top summer transfer targets." Then, a couple of weeks later, he quoted the player's agent, via a piece in Het Nieuwsblad, admitting talks had taken place. Last week, Law reported Chelsea would ask for £25 million for their Belgium international from any interested Premier League rivals, but...
Lukaku's expressed desire to play Champions League football—as stated in an article last week by the Daily Express' Ben Jefferson—might scupper any interest from Tottenham. Even so, it is understandable why the striker could be viewed around White Hart Lane as someone capable of taking Spurs to the next level.
Tottenham transcending their current status as an aspirational Premier League top-four contender to a perennial title challenger will not happen because of just one signing (not with the players realistically available to them). New boss Mauricio Pochettino has plenty of work to do in establishing a working environment where one player could make a notable difference.
Much of that will rely on getting the best out of the players already in his squad. The prospect of Spurs' current forward trio of Emmanuel Adebayor, Harry Kane and Roberto Soldado delivering the goals the team needs is not out of the question.
Adebayor and Soldado might find more consistency, while Kane's growing confidence could help him fulfill his youthful promise. Still, Lukaku might just be one of the known performers within their price range who can bring that extra bit of quality Spurs require to push forward.
Tottenham scored 55 times in the Premier League last season, 13 less than fourth-place Arsenal. Considering Liverpool scored 101 times and champions Manchester City 102, the need for more is understandable.
Lukaku is clearly not (yet) viewed as the all-round performer Jose Mourinho believes he needs to lead Chelsea's own quest for honours. That in itself is up for debate. As Squawka's Daniel Anwar detailed, aspects of Lukaku's game, besides his finishing, were either better or bore comparison with Adebayor and Soldado last season.
Even with the Tottenham pair's respective issues, it is commendable that a player who was still only 20 years old exceeded the performances of two experienced and notable strikers.
The work Lukaku could do in build-up play and occupying defences would, of course, be part of his appeal to Spurs as a focal point for their front line. But the main reason he is such a tempting acquisition is his aforementioned ability to find the back of the net.
To score the amount of goals he already has at such a young age is highly impressive. It is a good bet experience and maturity will see the former Anderlecht player get better in front of goal too.
Even at this summer's World Cup, there was a distinct improvement over the course of the tournament. The slightly lost Lukaku of the group stage changed into the striker who successfully interpreted and confidently changed the game with an assist and a goal in Belgium's last-16 win over the USA (though the greater space granted him by tired legs in extra time helped).
But even the Lukaku who netted 16 in 2012-13 and 17 last season would likely be useful to Spurs.
Save for Gareth Bale's 26 goals two years ago (21 in the league), it has been a rarity for a Spurs attacker to exceed the 20-goal mark. A player in Lukaku, who is showing signs of at least nearing that with some regularity, would provide welcome reliability for a Spurs side searching for it in the Welshman's wake.
Tottenham will need more than goals to be better this season. Better displays in defence and a more effective teamwide vision of playing will be needed too.
But a source of scoring like Lukaku might just be the kind of player who gives them the necessary edge to progress in today's competitive Premier League. Now we wait to see if Pochettino and the Spurs hierarchy believe that to be the case.