Rahman spent more than a year out injured after tearing his cruciate ligament at the African Cup of Nations with Ghana; an injury which has had a sufficient impact on his 18-month loan spell at the Bundesliga club.
The 24-year-old is looking for a six-month loan deal to revitalise his career and is currently fit to play despite only appearing for 327 minutes this season.
Chelsea are keen to recall him but they are currently well-stocked in the left back position, with both Marcos Alonso and Emerson Palmieri battling it out for a spot in Maurizio Sarri's defence.
Rahman was a £21.7m signing from Augsburg when he joined the Stamford Bridge club in August 2015, but he has yet to make the sufficient impact, having made only 23 total appearances for the Blues.
The defender is seen as an option to help Villarreal steer away from the Liga relegation zone, while Girona are outsiders for a Europa League spot.
Michy Batshuayi is also being touted around by Chelsea over a lack of game time at Valencia, having often found himself on the bench too often for the Spanish club.
The Belgium international scored nine goals in 14 appearances for the current Bundesliga leaders last season, but has only managed three in 18 matches for Valencia.