Flanagan's standout season for the Reds in 2013-14 saw the 25-year-old feature alongside Gerrard as Brendan Rodgers's side missed out on the Premier League title.
According to The Mirror, the Rangers boss wants to reunite with Flanagan following the expiry of his contract with Liverpool at the end of this month.
The defender was on the fringes of Jurgen Klopp's Liverpool squad, before being handed a 12-month community order in January for assaulting his girlfriend last year.
The newspaper says that Gerrard will offer Flanagan a chance to get his career back on track with a move across the border ahead of next season.
Flanagan, who has one cap for England, spent the latter half of last season on loan at Bolton Wanderers.