Barkley is expected to leave boyhood club Everton this summer after he turned down a new contract worth over £100,000 a week to remain at Goodison Park.
The England international has a year remaining on his Everton contract and is keen to experience a new challenge.
And bookmakers Betfair have today cut Arsenal's odds of signing Barkley from 4/1 to 2/1.
The Gunners are reportedly in the market for a new midfielder as they look to offload £10million midfielder Mohamed Elneny.
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Ronald Koeman has confirmed Ross Barkley will leave Everton this summer
Arsenal odds slashed to sign Everton star Ross Barkley
But the bookies reckon Arsenal's north London rivals Tottenham are more likely to land Barkley, pricing Spurs as 10/11 favourites.
Premier League champions Chelsea are also in the market at odds of 6/1, while Everton's Merseyside foes Liverpool are considered shock outsiders at 12/1.
Everton manager Ronald Koeman yesterday confirmed that Barkley will leave this summer but admitted the club are yet to receive a formal bid.
When asked whether he "100 per cent" expects to lose Barkley, Koeman said: "Yes. Yeah. His personal situation is not so difficult.
"We made a really good offer to sign a new contract, he declined that contract and told me he's looking for a new challenge. It's his decision.
"I need to respect that and we'll see what happens, because I heard from the board that there's not really an offer on the table for Ross."
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