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The Gunners midfielder is out of contract in the summer.
And Starsport have been told by bookies Paddy Power that there’s been a flurry of bets on the England international swapping north London for Merseyside.
The odds on him being snapped up by Jurgen Klopp have now halved and are 7/2 after punters lumped on the 26-year-old.
Paddy Power spokesperson Amy Jones said: “Could Jurgen Klopp be plotting another Emirates raid?
“He’s already had Alex Oxlade-Chamberlain and now he’s sniffing around Jack Wilshere.
“He’s out of contract in the summer – so Liverpool could be set to bag a bargain. Either that or another flop.”