The Everton forward has been the subject of interest from the Premier League duo in recent months and is set to move on this summer.
And it seems Chelsea are edging closer to winning the race for his signature.
According to the Independent, United made an enquiry over the possibility of signing the Belgian, and while they were not given a firm “no”, the Old Trafford club were told that a deal with Chelsea is very close.
They add a move for the talented striker is expected to cost upwards of £80m.
Lukaku's current wages of £80,000 a week are also set to be doubled when he completes his return to Stamford Bridge.
The 24-year-old was at Chelsea between 2011 and 2014 but failed to be given the chance to impress before he was sold to Everton by Jose Mourinho in 2014.
Romelu Lukaku is edging closer to a move to Chelsea Romelu Lukaku transfer odds: Where next for the Everton star? Tue, June 6, 2017
Where could Everton ace Romelu Lukaku go next, according to Skybet odds?
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Arsenal – 33/1
But having proved himself as one of the Premier League's top goalscorers, netting 25 goals last season, Chelsea want him back in his prime.
Lukaku today admitted he had made a decision on his future but refused to publicly reveal which club he would be playing for next season.
"My agent knows what's going to happen," he told Sky Sports.
"I know what I want to do, and whenever something happens, you guys will know."
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Lukaku also admitted that playing in the Champions League is an important factor for him.
Romelu Lukaku looks set to snub Manchester United to join Chelsea
“The most important thing is: I want to win trophies," he added.
"We are now talking to the club. As for the rest… I’m looking ahead. What I would like most to play in the Champions League and try to win the Premier League once. Or better: a few times. That would be the most beautiful thing.
“That’s important for my progress as a player. I don’t want to stay at the same level. I want to improve and I know where I want to do that.
“We’ll see what happens.”