Wilshere has fought his way back into the Arsenal first-XI this season, but he is currently set to leave the club for free in the summer with his contract set to expire.
He has started the last six games for the Gunners and scored his first Premier League goal since his return to help the Gunners to a 2-2 draw with Chelsea on Wednesday night.
Wilshere admitted following the clash that there has been ‘no progress’ in his talks with the club – a new contract is reportedly on the table, but the midfielder wants assurances of regular football before he commits to a deal.
And Seaman has urged Arsenal to resolve the situation, insisting they cannot afford to let a player of his quality leave the club.
“Arsenal would be silly not to offer him a new contract,” the former goalkeeper told the Alan Brazil Sports Breakfast.
“I always said, Jack has got some magic, sometimes he reminds me a bit of Paul Gascoigne, he’s got that pass to unlock defences.
“You don’t want to let players of that quality go. They see things other players don’t and Jack is definitely in that league.”
Seaman also insists Wilshere’s return to fitness and form should see the midfielder return to the England fold ahead of this summer’s World Cup in Russia.
The 25-year-old hasn’t played in a Three Lions shirt since their disastrous European Championship exit to Iceland in June 2016, but Seaman believes he is a shoo-in to return for their next major tournament.
Asked if he can play his way back into the squad, the ex-England number one added: “The way he’s going, I can’t see why not. He’s playing well, he’s fit and he looks a threat.
“Gareth Southgate said before that he couldn’t pick him if he wasn’t playing, but now he’s playing and he’s producing, so there’s no reason why he shouldn’t get in that squad.”