Liverpool and Chelsea are also reportedly interested, however it is understood that Juventus are firm favourites to land his signature.
Juventus hold a significant advantage over their rivals. The Wales international will be available on a free transfer, meaning Juve can agree a pre-contract with lucrative terms in January - whereas the Premier League clubs will have to wait until May.
Despite being an established and influential member of Arsenal's dressing room the 27-year-old's transfer talks with 'The Gunners' have broken down, with Unai Emery reportedly not ready to meet Ramsey's demands.
Without a transfer fee, Ramsey could command wages close to £250,000 a week in Turin.
Despite the lucrative offer from Juventus, winners of the last seven Serie A titles, it is also understood that Ramsey may prefer to stay in England with his young family — but the prospect of a near-guarantee of medals with Juventus and the opportunity to play alongside Cristiano Ronaldo could be crucial factors.
Ramsey has made eight Premier League appearances this season, assisting with three goals.
The former Cardiff City midfielder also found the back of the net for the first time last match, scoring in Arsenal's 1-5 demolition of Fulham at Craven Cottage.
Ramsey has won three FA Cups and two Community Shields at the Emirates.