The 27-year-olds current deal with Arsenal expires at the end of the season and the midfielder is set to leave the club after the Gunners withdrew their offer of a new contract.
Ramsey has attracted interest from several clubs, including Chelsea, Manchester United, Paris Saint-Germain and AC Milan.
But multiple reports in Italy claim that Juventus are in the driving seat for Ramsey after their latest offer to the midfielder.
Ramsey has been offered a £9 million-a-year deal by the Serie A champions to join them on a free transfer next summer.
And Inter have now pulled out of the race to sign Ramsey after being blown out of the water by Juves offer.
Juventus signed Emre Can on a free transfer from Liverpool in the summer after his contract expired.
And the Italian champions are looking to bolster their midfielder even further with Ramseys arrival.
Juventus will be able to sign Ramsey on a pre-contract agreement from the start of January.
More: Arsenal FC