The Red Devils have agreed a £75m fee with Everton for the Belgium international.
Starsport understands United have also agreed personal terms and a deal could be announced later on this week.
Lukaku, 24, is Antonio Conte's top summer target and the Italian is desperate for the Blues to re-sign the striker.
And according to the Independent, Chelsea could make a bumper bid to land the Everton star.
They say the Toffees expect the Blues to aggressively challenge United for Lukaku's signature.
United are yet to make a bid for the striker and The Independent reckon Chelsea maintain a deal is not done.
The Blues could respond to the Red Devils agreeing a fee with a mammoth offer of their own in hope of securing Lukaku.
However, it would take around a world-record bid to land the Everton star ahead of United.
Lukaku is set to earn around £200,000-a-week if he moves to Old Trafford.