The deal is now said to hinge on Dybala agreeing terms with United.
His agent is understood to be in London for talks with United over a move to Old Trafford.
Dybala is valued at €100m (£91.8m) and is keen to stay but wants to meet with Maurizio Sarri when he returns from his holidays on Thursday before making a final decision.
United manager Ole Gunnar Solskjaer, speaking after Tuesday’s pre-season win over Kristiansund, would not be drawn on a potential deal for Dybala but confirmed new arrivals could be in the offing.
“I’m not here to talk about any rumours or speculation about other team’s players,” said Solskjaer.
“But of course, we’re working on one or two cases, as I’ve said before.
“There’s another 10 days before we start the league and hopefully we can announce a fresh face or two.”
Juventus must convince Dybala to make the move to Manchester, as United would require a replacement for Lukaku.
If Dybala is unable to agree terms on a move to Old Trafford, Lyon striker Moussa Dembele is also on United’s shortlist to replace Lukaku.