Lukaku had appeared set for Old Trafford when it emerged a blockbuster offer of £75 million had been accepted by current club Everton.
But Chelsea will not give up on their top striking target, as Goal understands they have made an identical bid to United's.
The delay in making a formal offer, however, means the Red Devils remain in the driving seat for Lukaku, who bagged 25 goals in last season's Premier League campaign.
News of United's push was not well-received in west London, where the Belgium international has long been linked with a return to his former side.
Some reports even claimed the failure to land Lukaku had strained manager Antonio Conte's relations with the Chelsea board, after being assured his transfer ambitions would be matched in the current window.
The Blues will keep up their interest until the bitter end, but have compiled a shortlist of alternatives should their last-minute sortie fail to succeed.
Real Madrid striker Alvaro Morata is one of the men considered as a potential replacement for Diego Costa, who has been declared surplus to requirements by Conte and is expected to move away this summer.
Ironically, Morata had been tipped to join Jose Mourinho at United, and it was the club's frustration at the stalled move that led them to turn their attention instead to Lukaku .