The Welsh global is in the final year of his contract and the Mirror claims Ramsey has been willing to put pen-to-paper over a new deal with the club also understood to be confident in recent weeks that an agreement would be reached following extensive talks with the player's agent.
This puts the two Serie A clubs in direct competition with each other to secure his signature.
And Emery admitted the 27-year-old has to do what was best for himself - while suggesting that focusing on his displays for Arsenal will provide the best platform to do so.
"Although it is very hard to do - the hardest decision of my life - I believe that, after 10 years, it is the right time to step aside to allow new leadership, energy and ideas to take the club forward into this exciting new era".
However, negotiations over a new deal between Ramsey's representatives and Arsenal officials have come to a sudden halt.
Asked if that would have an impact on the player, Emery said "I think not".
Martial, Bailly, Pereira join Pogba to rebel against Mourinho
The deteriorating relationship between Mourinho and Pogba has been a talking point throughout most of the calendar year so far. Paul Pogba's older brother Mathias has joined Tours in the French third tier after spending more than a year without a club.
They add Ramsey was chasing a contract worth £200,000-a-week - which would provide parity with Pierre-Emerick Aubameyang and Henrikh Mkhitaryan, but still be some way below German ace Mesut Ozil.
Manchester United, Chelsea and Juventus are all keen to sign him - and the Wales global would consider a move overseas.
"I consider each player an important space in the squad".
"Barca play very good football and Arsenal want to do the same", Ramsey told Marca.
Arsenal could be forced into selling the player during the January transfer window if they want to avoid him leaving for nothing.
Other interested clubs include Chelsea, who showed interest in Ramsey over the summer before signing Mateo Kovacic on loan from Real Madrid, while Manchester United are likely to be in the running to sign a player who famously rejected them to join Arsenal when he was 17.