According to The Mirror, Rooney is the Blues' main transfer target once more as they continue to rebuild their squad, with the current form of their strikers meaning a world-class frontman is high on their list of priorities.
It's understood Manchester United are yet to offer Rooney a new contract, meaning next summer he will enter the final year of his existing deal that expires in 2015.
Should that remain the case, Rooney's bargaining power will be considerable and any bids from Chelsea—or another elite club for that matter—could very well result in his Old Trafford departure.
Indeed, were that to happen, the fabric of the Chelsea team as we know it could look very different come the start of 2014-15.
That would give Chelsea two players who already have a combined 18 goals in all competitions thus far this season—a stat in stark contrast to Fernando Torres, Samuel Eto'o and Demba Ba, who continue to struggle in front of goal.
Given the different attributes each would bring Chelsea, a Rooney-Lukaku double act would mean far more options than what they have right now.
Mourinho has thrown caution to the wind at various stages of 2013-14 by adding an extra striker late in games when his team has been chasing a result. He hasn't started Torres, Ba and Eto'o together, however.
With the three attacking midfielders behind them, it's an option he cannot consider as Chelsea would be severely weakened elsewhere to accommodate a strike partnership of players whose return hasn't warranted it yet.
It would work slightly different with Rooney and Belgian Lukaku, though.
Rooney has shown throughout his career he can lead the line, playing through the middle to be the fulcrum of the attack for his club. Lukaku himself did it last season for West Bromwich Albion and has continued that trait with the Toffees.
Their combination would be an interesting one. Would it be Lukaku furthest forward, playing off Rooney? Or the other way around, with the Englishman benefiting from Lukaku's physicality, dropping off him to exploit the space in behind the defence?
In many ways, it would be a partnership akin to Liverpool's successful spell with Emile Heskey and Michael Owen over a decade ago—only Chelsea would have two players of better quality fulfilling the roles.
The Liverpool of the Heskey and Owen era had too many shortcomings elsewhere to scale the heights the club had in the 1970s and 1980s, but it was their partnership up front that allowed the club to overachieve, winning FA Cups and even European trophies.
Heskey was often criticized as an individual, but with Owen alongside him, he proved lethal for the Reds. England even benefited at times, with their partnership helping the Three Lions to World Cup qualification in 2002 and a memorable 5-1 victory over Germany in the process.
Would a Rooney-Lukaku partnership be better than Chelsea's current options up front?
The point is, defences struggled to cope and it would be an equally daunting prospect for Premier League defenders to face Rooney and Lukaku on a weekly basis.
Chelsea's current 4-2-3-1 formation is more about getting the most out of the likes of Oscar, Juan Mata, Eden Hazard and the rest of their current crop of talented attacking midfielders, than it is the strikers.
Switching to a 4-3-1-2, for instance, to accommodate two strikers would change the emphasis somewhat, giving the potential for more goals. It would impact the quantity of No. 10s Mourinho could play, yet if it produces a prolific front line, the change of tact would have been well worth it.
They just need to sign Rooney first.
Garry Hayes is Bleacher Report's lead Chelsea correspondent and will be following the club from a London base throughout the 2013-14 season. Follow him on Twitter here @garryhayes