Slaven Bilic has already strengthened his side this summer and the addition of the talented midfielder looks to be a real possibility.
While the move perhaps may not come to fruition, a number of people have tipped Wilshere to represent the club he supported as a boy.
Here is what Wilshere has said about the Hammers, as well as what others have said about a possible move to east London.
Wilshere on West Ham…
“My family have always been West Ham fans, so growing up I used to go and watch them and so I was a West Ham supporter,” Wilshere said back in 2011.
“I remember my first game was against Coventry, in 2000, Di Canio scored a hat trick and they won 5-0 so I enjoyed it.
“I used to look up to him for some of the goals he scored. My favourite goal of his was a volley against Wimbledon.
“The fans at Upton Park are great. They are bottom of the league yet they fill it every week and it’s nice to go and play there because there’s always singing. It’s loud and that’s what you want as a footballer.”
Slaven Bilic on Wilshere…
“There is no point discussing him, I don’t discuss transfers,” Bilic said when quizzed on a potential move for the midfielder.
“Of course if we are talking about Jack Wilshere as a player, that’s different.
“Jack Wilshere is a great player with great ability but because of injuries had to go on loan to Bournemouth.
“He is a great player at a good age also – a great age.”
Ray Parlour on Wilshere…
“I know he’s not playing at the moment, but I think a lot of clubs would be very interested in him,” former Arsenal midfielder Parlour said.
“The most important thing was to stay fit and he’s done that. He’s had a few niggles but every player gets them but he’s stayed away from long term injuries.
“I think West Ham have been mentioned, his dad is a big a West Ham fan, that might be a move. Their midfield does need a little bit of strengthening.
“Bournemouth will be interested too as I am sure he’s been great for the dressing room. He wants to get back in the England squad so he needs to play on a regular basis. whether he gets it at Arsenal, I don’t know.”
Tony Cottee on Wilshere…
“All we need to now is sign Jack Wilshere. I think he’d be a great addition,” admitted Cottee.
“You’ve just got to keep him fit, that’s all you’ve got to do. He’s a £50m player when fit.
“He’s had a lot of problems and I feel for the boy – but they’ve just got to keep him fit.”
Would you like to see West Ham sign Jack Wilshere? Let us know in the comments section below.