Lukaku is set to leave Goodison Park this summer after refusing to sign a new contract and the Toffees hope to recoup £90million for his services.
Reports from earlier in the month suggested Lukaku was closing in on a return to Stamford Bridge, but the Daily Mirror say a deal is yet to be struck.
Premier League champions Chelsea desperately need to sign a striker ahead of Diego Costa’s seemingly inevitable exit but United and Bayern may yet launch moves with Lukaku’s agent, Mino Raiola, in contact with both clubs.
Despite this, the Blues remain frontrunners to sign the Belgium talisman, who they sold for £28m in 2014 after three uneventful years at the club.
Romelu Lukaku's Premier League season Games played37Goals scored25Assists6
Lukaku is one of the most in-demand players in Europe after another fine season for Everton (Picture: Getty)
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Jose Mourinho’s United have expressed interest in Lukaku on the back of the 24-year-old scoring 25 goals in the top-flight last season.
The Portuguese boss is looking to add a star striker to his squad at Old Trafford after Zlatan Ibrahimovic was released by the Red Devils following an impressive debut season in England.
German giants Bayern, meanwhile, may be forced to enter the market for an attacker after Robert Lewandowski emerged as a surprise target for Antonio Conte at Chelsea.