The Red Devils are reported to be edging closer to tying up a deal for the England U21 international.
A change in approach to recruitment at Old Trafford has seen potential favoured, with a £15m move for Wales international winger Daniel James already completed.
Wan-Bissaka may be the next to arrive, and Shipperley believes an agreement will suit all concerned.
He sees United getting a player of considerable promise, while Palace will be generating a sizeable fee for a player in a position that they already boast suitable cover in.
The Eagles legend told Love Sport Radio: “I think it’s good business for a right-back that has made 42 appearances. It’s a great deal for the club. This is football at the moment.
“There’s not a bidding war for him. Manchester United are the club. No-one else is coming in for him so you’re not going to have this bidding war. I think £50m or £55m is a fair deal.
“The fans aren’t going to like this but what they’ve got to realise is that this kid could still be in the Under-23s. He only came on the scene because we had no-one else to play right-back. He came in and he has made that position his own.
“He’s a great player but at the end of the day, he’s a right-back. He’s not a centre midfielder or a centre forward like Wilf [Zaha]. He’s a right-back and I think we’ve got a replacement in Joel Ward, who is not as good as Bissaka but he can certainly play right-back and do a job.”
Shipperley added, on a fee that could make Wan-Bissaka the most expensive English player in history: “Back in the day it was centre forwards [who went for big fees] because they were the ones that won you games. There was no talk of massive money for defenders and goalkeepers. It was really just strikers.
“As kids, you wanted to be a striker. But now you might as well go and play left-back and study that, make it your position because it’s not just about centre forwards anymore.”
Wan-Bissaka is not the only Palace player generating talk of a big-money move this summer, with speculation also surrounding Wilfried Zaha once more.
He, too, has been linked with a switch to United, having previously flopped during a forgettable spell at Old Trafford, but Shipperley doubts two prized assets will be offloaded in the same window.
“There will be uproar if Wilf and Bissaka both go,” added the former frontman.
“I can understand this one [Wan-Bissaka] because I don’t think Crystal Palace are a club at the moment who can turn down that money.
“I thought it was going to be the other way round because I thought Wilf would go and we’d keep Bissaka.
“But I would imagine with this looking like it’s going to get over the line, Wilf will stay. If he doesn’t, I think the fans… you can’t lose two big players like that unless we’ve got something up our sleeve where we can go and buy some able replacements.”