Lukaku is expected to leave Everton during the summer transfer window after telling Ronald Koeman he did not plan to sign a new deal with the Toffees.
Everton have identified a potential replacement for Romelu Lukaku who is speculated to be leaving the club this summer.
The Premier League's top scorer told Everton earlier this year he would not sign their latest contract offer, although sources said at the time talks would continue.
With both Chelsea and United reportedly interested, The Sun note that the Belgian worldwide could snub his former club as he has his concerns over how he would fit in at Stamford Bridge with regards to Antonio Conte's style of play.
The 23-year-old has been strongly linked with a return to Chelsea for many months, however reports on Monday claim the 23-year-old is no longer interested in re-joining the Blues and now favours a move to Old Trafford instead.
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Further, the Belgian "believes he is more valued by United" but "desperately wants" to play in the UEFA Champions League, something Chelsea are guaranteed to play in while the Red Devils could be relying on winning the UEFA Europa League after losing to Arsenal on Sunday.
"But if you play at the highest level, your finesse on the ball in the final third, your decision making has to be absolutely spot on".
Lukaku has also been linked with a return to former club Chelsea, but is now under contract at Goodison Park until 2019.
"Yes he will bring power, he'll bring some strength but if you look at the strikers United have had [over the years] does he fit in that same line of striker?"