The veteran comes off contract in June.
The Mirror says the Rs have headed the list of suitors for a while.
However, QPR will have to get through the play-offs to stand a chance of signing Ferdinand. There are also possibilities abroad with LA Galaxy preparing an offer along with Turkish clubs Galatasaray and Besiktas.
But Ferdinand - who endured a frustrating time under the David Moyes regime - feels he can still cut it in the Premier League.
For breaking stories and all the great banter like us on Facebook: facebook.com/tribalfootball