The Arsenal star is set to leave the Emirates either in January or next summer, when Ramseys current deal expires.
Chelsea, Manchester United and Liverpool are chasing the transfer, but it is the foreign clubs who have made the first moves.
Ramsey is free to speak to oversea clubs in January and can sign a pre-contract.
Juventus want Ramsey to see out his contract with Arsenal, so that he can join them on a free transfer in the summer.
Ramsey has been offered a £200,000-a-week deal to join Juventus and are happy to sign the 27-year-old up to a four-year contract, which would mean the Gunner would collect £40m in total before tax.
Several English clubs are monitoring Ramseys situation, but may not be able to compete with the wage package on offer from Juventus.
Ramsey is reportedly keen to stay in the Premier League, but the lure of a lucrative deal in Italy may be too much to turn down.
Arsenal are prepared to let Ramsey leave after withdrawing their contract offer at the request of Unai Emery.
Emery is thought to want to use the funds that could be spent on tying Ramsey down to a new deal on his own signings.
Arsenal could offload Ramsey in January, and are preparing for the prospect of losing the midfielder mid-way through the season.