United have already had an opening £40million offer turned down for the young Englishman this summer.
Sky Sports understand that Crystal Palace are bargaining for more than £50m for their academy graduate.
While United step up their chase, such is Ole Gunnar Solskjaer’s adamancy to find a long-term replacement for Ashley Young, they have been served a catalyst.
That is because the Eagles are already searching for a successor to Wan-Bissaka, according to HLN.
“Crystal Palace have held exploratory talks over Belgian international Timothy Castagne,” journalist Kristof Terreur tweeted.
“He’s one of the main candidates if Aaron Wan Bissaka moves to Man United.
“Castagne is currently undecided over his future: CL with Atalanta, the PL or being a back-up at Napoli.”
Castagne, 23, is two years Wan-Bissaka’s senior and was a regular in Atalanta’s impressive Serie A season, which secured them Champions League football for the first time.
The Belgian can switch between left- and right-back, unlike Wan-Bissaka, who is far more comfortable on the right flank.
Wan-Bissaka has told Palace he wants to move to Old Trafford, but the club are trying to include as many demands as possible in the deal.
Intriguingly, they are hopeful of removing the sell-on fee United sealed when selling Wilfried Zaha back to Selhurst Park.
The opening offer contained several potential bonuses and additional payments which could benefit Palace in the long-run but they believe United will stump up more cash.
Wan-Bissaka is currently in Italy for the Euro U21s championship while negotiations continue.
“Let’s go #YoungLions,” the youngster wrote on Twitter with a picture of him boarding the plane, before talking up the “Big game on Tuesday” when England face France in their opener.