Lukaku's form for Everton has seen him attract interest from the Premier League winners as well as from United manager Jose Mourinho, with the Belgium international scoring 25 goals and registering six assists in the league last term for the Toffees.
The striker was all but set to return to Stamford Bridge after he emerged as a priority target for Chelsea manager Antonio Conte in this summer's transfer window.
However, according to the Daily Mail, United are set to hijack Chelsea's move for Lukaku as Mourinho looks to bolster his attacking options for the next season.
Strangely enough, Mourinho was in charge of Chelsea when he sanctioned the striker's sale to Everton in 2014, a year after joining them on loan.
Everton value him at around £100m ($129.5m) and if the deal goes through, it would eclipse the world-record £89m ($115.2m) fee paid by United to sign Paul Pogba from Juventus last summer.
The Mail reports that one of the reasons Everton are not too keen on selling the striker to Chelsea is the relationship between the two clubs, which have soured since the former's failed efforts to sign John Stones in 2015. The England international eventually made the move to Manchester City last summer.
It is believed that Mourinho's United are now in the driver's seat to secure the services of Lukaku as the former Chelsea striker will now be heading towards Old Trafford, instead of Stamford Bridge.
Rooney set for Everton return
With Everton set to sanction Lukaku's sale, they are in the market to further strengthen their attacking line-up after completing Sandro Ramirez's signing. According to rumours, the Merseyside club are looking at bringing United captain Wayne Rooney to Goodison Park.
The England international left the Toffees for the Red Devils in 2004 and is currently United's all-time leading goalscorer. However, Rooney is no longer involved in Mourinho's plans at Old Trafford and the Portuguese tactician is ready to allow the forward to leave the club this summer.
Rooney's agent Paul Stretford held talks with Everton chairman Bill Kenwright in London. The player has also publicly confirmed that if he leaves United, he will only play for Everton in the Premier League.