United manager Ole Gunnar Solskjaer is targeting right-back Wan-Bissaka as part of his summer overhaul, but United have had an initial offer of £35 million plus £5m in add-ons turned down.
Aaron Wan-Bissaka broke into the Palace team at the back-end of the 2017-18 season.
The news comes after other claims this weekend that United had already submitted a 'substantial bid', so it seems likely that this story has legs.
Premier League champions Man City are also interested in signing Aaron Wan-Bissaka but they are monitoring the situation closely.
Should the Englishman be signed, it could also spell the end for Young's time at Old Trafford.
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"He's obviously another one linked with moving away but I'm just a bit concerned with Aaron". He probably needs more games. The Eagles have not ruled out letting the England under-21 worldwide leave but are planning to hold out for a guaranteed £50m with a series of add-ons that could take the deal past the £60m mark.
"You remember with Walcott and those types of players who came through at Southampton - even [Gareth] Bale or [Alex] Oxlade-Chamblerlain - they came early and it took them years to find their feet".
However, Dalot hasn't exactly impressed in the few appearances he was granted last season, meaning he is yet to prove that he is good enough to start week in and week out.
"We're not naive. We understand football works that way, but he has signed a long-term contract and we signed him to be a long-term player with us".