Despite having been in talks regarding fresh terms at Emirates Stadium for some time, the 26-year-old continues to head towards free agency.
Departing Gunners boss Arsene Wenger has stated on a regular basis that he expects an agreement to be reached, but he is heading for the exits and may be followed by Wilshere.
Morrison believes Selhurst Park would be an ideal next port of call for the England international and is hoping to see his former club express an interest at some stage.
Quizzed by Express Sport on whether he would be looking to do a deal for Palace: "100 per cent. I’d take Jack Wilshere tomorrow.
"I think he’s terrific. If you could get him injury-free, what a signing that would be for Crystal Palace.
"Obviously he’s a London boy so hopefully he wants to stay in London and play and I think Palace would be the right club.
"And hopefully if Steve Parish can make it happen, it would be magnificent if Roy Hodgson wanted him.
"But I don’t know why you wouldn’t want Jack Wilshere. When he’s injury-free, I think he’s still got a lot to offer and I think he’s a very good midfielder."
Morrison believes Roy Hodgson will be backed in the transfer market this summer, with Palace prepared to make the funds available for players like Wilshere as they seek to avoid a repeat of this season’s scramble for Premier League survival.
"They’ll definitely try to spend, without shadow of a doubt,” added a man who took in two productive spells with the Eagles during his playing career.
"They won’t want to be in that situation that they were in this season, fighting relegation, even though in the end they could finish in the top 10, which would be a great achievement. But you don’t always want to keep fighting relegation.
"I think they’ve got the real man in charge now, Roy Hodgson. I think Steve Parish will back the manager again.
"And I don’t think there’s a lot needs to be done. But I think three or four new players coming in, because we don’t know if they’ll keep [Ruben] Loftus-Cheek, who’s been brilliant since he came back from injury.
"There’s a lot of changes that should be happening at Palace but the main one I think is you’ve got to try and keep Wilfried Zaha."