Manchester United and Juventus have agreed a swap deal in principle involving Paulo Dybala and Romelu Lukaku, according to Sky in Italy.
The deal is now said to hinge on Dybala agreeing terms with United.
Jorge Antun, one of the player's representatives, 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 head coach Maurizio Sarri before making a final decision, according to Sky in Italy. He will hold a meeting with the former Chelsea boss this week.
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.
Should the Argentine refuse to leave Turin, Juve would have to come up with a cash deal but still offload one or more of their current strikers.
Pavel Nedved, the Juve vice president, was questioned on Dybala and Lukaku on Monday by Sky in Italy.
He said: "We have some offers for Paulo Dybala but we'll wait to decide about his future. Lukaku? We always try to get players but I don't want to speak about Lukaku or others."
Juventus are understood to have moved ahead of Inter Milan in the race to sign Lukaku, Sky Sports News understands.
Inter director Giuseppe Marotta insists the Serie A club "are still working" on a deal to sign Lukaku.
He also said Inter made "a fair and important offer respecting the value of the player", but it is understood that bid of £54m was immediately rejected by United earlier this month.
Lukaku further fuelled speculation over his future by posting an image on social media alongside his agent Federico Pastorello over the weekend with the caption "soon to be continued".
The Belgian is valued at more than £79m, what United paid to Everton in 2017, and it is unlikely Inter will get close to this without offloading players as they are mindful of working within Financial Fair Play rules.
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