The Premier League duo have both been linked with a move for the Everton forward, who has hinted that he is seeking a move away after expressing a desire to win titles and trophies. Ronald Koeman is keen to keep his top scorer at Goodison Park, but is aware that interest from the top clubs has already turned Lukaku's head.
Everton holds the cards when it comes to the negotiation table owing to the two years remaining on his current deal and have already slapped a £100m ($128m) price-tag on the striker. United and Chelsea are not short of funds, but are unlikely to bow down and match their valuation for Lukaku.
According to the Sun, the Blues hold the advantage in the transfer race with the Belgium international having told pals that he prefers a return to Stamford Bridge rather than working with Jose Mourinho at Old Trafford.
Lukaku joined Chelsea as an 18-year-old from Anderlecht and made 10 appearances for the Blues in three seasons, which included two loan spells at West Bromwich Albion and Everton. It was after his second loan spell with the Toffees that Mourinho, who was in is his second spell as the Blues boss decided to allow him to join Everton on a permanent basis.
Chelsea are sweating on the future of Diego Costa with Chinese Super League clubs interested in the Brazil-born Spain international and are looking for an alternate incase their main striker departs for pastures new. Antonio Conte believes the Premier League's current top scorer will fit the bill and is ready to sanction a move in the summer.