The Welshman has been linked with a number European giants since it was confirmed he would be leaving the Emirates on a free.
Ramsey's talks of a new contract fell through recently leaving elite clubs eyeing a bargain move – with Bayern Munich just 7/2 to sign the 27-year-old.
The Bundesliga champions have leapfrogged Arsenal's Premier League rivals Liverpool, Manchester United and Chelsea in the market.
The competition for Ramsey's signature is fierce with AC Milan and Juventus also firmly in the running.
Alex Apati of Ladbrokes said: "Ramsey's struggling for game time at the Emirates but he could have hit the jackpot with Bayern now reportedly keen and leading the way for his signature."
Ladbrokes: Aaron Ramsey next club
Bayern Munich – 7/2
Liverpool – 4/1
Man United – 5/1
AC Milan – 5/1
Juventus – 6/1
Chelsea – 7/1
Wales boss Ryan Giggs has emphasised how his midfielder will have plenty of clubs to choose from.
Giggs told Sky Sports: “He won't be short of offers as he's a talented player.
“He's one of those players that, if he plays a full season, will get 10-15 goals from midfield and that's a very attractive player to have in any side.
“He's friends with Gareth Bale so obviously he'll be able to tell him what it's like to play abroad and Aaron's certainly got the talent to play anywhere in Europe but that will totally be his decision.
“As long as he's playing regular football, that's all I really care about.”
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