The midfielder is facing further competition for the central midfielder role he craves at the Emirates.
The Welshman has been handed his chance in central midfield by manager Arsene Wenger this season and has largely impressed.
However, the Gunners are looking to bolster their midfield ranks this summer, with Borussia Monchengladbach midfielder Granit Xhaka their number one target.
They also have an interest in Real Madrid midfielder Toni Kroos should he be allowed to leave the Bernabeu at the end of this season, according to the Daily Mail report.
Should either of those arrive, that would mean Wenger has serious options for his central midfield, with Francis Coquelin, Jack Wilshere, Mohamed Elneny and Santi Cazorla all wanting central roles all competing for just two places.
Such an eventuality would likely see Ramsey returned to the right midfield role he has occupied for much of his time at the club.
However, he has often stated his desire to play in central midfield and that wish could put his future at the Emirates in doubt, with clubs in Europe and the Premier League sure to be keen on his signature if he is put up for sale.