The central midfielder has opted to leave the Emirates at the end of his current contract.
Thatâ€™s after discussions with new Arsenal manager Unai Emery over his role in the side.
And Parlour thinks Wilshere could move to West Ham because his father supports the Hammers.
â€śJack has done brilliantly for Arsenal,â€ť he told talkSPORT.
â€śI know heâ€™s had his injury problems, but Iâ€™m sorry to see Jack leave because I love seeing homegrown players come through the ranks.
â€śI think his dad is a West Ham fan, so that might be the place he ends upâ€ť
Arsenal legend Ray Parlour
â€śHe knows what itâ€™s like to play for Arsenal and itâ€™s a big decision heâ€™d made to leave the club.
â€śAfter I left the club there were two players I always saw who stood out as youngsters and I thought they would go on and have unbelievable careers â€“ one of them was Cesc Fabregas and the other was Jack Wilshere. He wasnâ€™t fazed by anything but his injures have just taken their toll.
â€śJack needs to play football â€“ heâ€™s 26 years old, thereâ€™s no good him sitting on the bench or in the stand.
â€śNice would be an interesting move, but heâ€™s got two young children so staying in London might be ideal him.
â€śCrystal Palace and West Ham have been talked about and I think his dad is a West Ham fan, so that might be the place he ends up.
â€śThere will be so many clubs in for Jack and whoever gets him will be getting a very, very good player.â€ť
Wilshere struggled with injury again last season although he did make 20 Premier League appearances.
The midfielder missed out on a spot in the England squad for the World Cup though.