Kostas Manolas's agent John Evangelopoulos has revealed that Roma rejected a £35m bid from Arsenal last summer.
The 25-year-old is believed to have attracted interest from Arsenal's rivals Manchester United, while Everton are also rumoured to be considering a move for the Greek international.
Roma managed to keep hold of the defender, but the player's representative has hinted that a transfer could happen at the end of the season.
"Over the summer Roma rejected an offer of €40m (£35m) from Arsenal," Evangelopoulos told Greek radio station Sport FM. "The Gunners were interested but Roma's demands were too much for the English club.
"Probably a sale in June? I cannot say for sure, but probably there will be something this summer, but in general in the world of football, it is difficult to make predictions."
Manolas moved to the Stadio Olimpico from Olympiacos in 2014.
