It was believed that the Blues had won the race to sign their former striker, whom they sold to Everton two seasons back for £28m ($35.3m) after he impressed for the Toffees last season.
But the Mirror, citing sources close to the player, reports that no deal has been struck with the Premier League champions about a return to Stamford Bridge which will give United and Bayern hopes of signing Lukaku. The Belgium international has made it clear that he wants to leave as he seeks Champions League football, something the Goodison Park outfit cannot provide.
Ronald Koeman, meanwhile, does not want the striker to leave and is keen on keeping him at Everton. Lukaku still has two years to run on his current deal with his present employers and thus they will hold all the cards when it comes to negotiations with interested suitors.
Chelsea are said to be leading the race for his signature, but the report claims that the Merseyside club are not willing to lower their valuation. Everton want £90m ($113.6m) in order to allow the striker to leave the club this summer, which will make him the most expensive player in the world eclipsing the £89m United paid Juventus for Paul Pogba last summer.
The Stamford Bridge outfit are looking for a forward to replace Diego Costa, who is almost certain to leave after Conte made it clear that he is not part of his plans next season. Lukaku scored 25 goals in 37 Premier League games last season and is more than capable of leading the line.
Similarly, Jose Mourinho is looking for a striker to fill the void left by last season's top scorer Zlatan Ibrahimovic, who picked up a long-term knee injury, which eventually saw him being released by the club following the expiry of his one-year contract. United have been heavily linked with a move for Real Madrid's Alvaro Morata, but the Mirror report claims that they have maintained contact with Lukaku's agent over a potential transfer to Old Trafford.
Bayern are recent entrants into the race after it emerged that their last season's top scorer Robert Lewandowski is not happy with the club and his teammates as they failed to help him on the final day of the campaign to win the golden boot. The Polish forward lost out on the award to Borussia Dortmund's Pierre Emerick-Aubameyang by just one goal and it has not gone down well with him.
Meanwhile, according to another Mirror report, Chelsea have been alerted about Lewandowski's unhappiness at Bayern and are reportedly considering making a move for the forward. If Everton are reluctant to lower their valuation, the Blues could move on to other targets and the Poland international will be an upgrade as he amassed 43 goals in 47 games last season.