Lukaku is a target for Juve's Serie A rivals Inter Milan and sources have told ESPN FC he is keen to join the Nerazzurri and work under manager Antonio Conte, who he recently labelled the "best manager in the world."
Injuries have prevented Lukaku from making any appearances during United's preaseason tour of the Far East and, so far, the Old Trafford club's £80 million valuation of the Belgium international has not been met.
Despite spending €75m to sign Matthijs de Ligt from Ajax, Juve are looking for one more big signing and sources have told ESPN FC they are preparing to offer Dybala to United as part of a bid for Lukaku. Though, it remains unclear whether Dybala would be interested in moving to Old Trafford.
Tottenham have also been linked with an £80m move for Dybala in the English media.
Sources told ESPN FC that United have already rejected a £54m from Inter for Lukaku. One way the San Siro club could raise funds to meet United's valuation of the the ex-Chelsea forward is to offload Mauro Icardi, who has been told he has no future at the club.
Icardi has been heavily linked with a move to Juventus -- while Napoli are also monitoring the situation -- but so far there has been no official bid for the Argentine.
Lukaku joined United from Everton in 2017 and was the first-choice forward under Jose Mourinho.
However, the Portuguese manager's replacement Ole Gunnar Solskjaer appears to prefer Marcus Rashford in attack.