The former Arsenal midfielder is out-of-favour at Italian giants Juventus.
According to Italian journalist Gianluca di Marzio, Rangers could be a possible option for the player.
It is reported that "negotiations are underway” with the Ibrox side.
Ramsey has plenty of possible suitors in England with Burnley and Wolverhampton Wanderers amongst those linked with a move.
The 31-year-old has featured just five times this campaign under Massimiliano Allegri and he still has 17 months left on his lucrative contract.
Rangers have reportedly been in the market for more midfield creativity having added Amad Diallo who netted on his debut in the 3-3 draw with Ross County at the weekend.
They have been linked with Manchester City starlet James McAtee.
Meanwhile, it is understood Polish right-back Mateusz Żukowski is in Glasgow ahead of a £500,000 move from Lechia Gdansk.