Rahman joined Chelsea for a deal worth £22m in 2015, but he has struggled to carve out a niche for himself at Stamford Bridge.
He has made just one senior appearance for Chelsea and has had a succession of loan spells away from Stamford Bridge since then.
He had spells at Schalke, Reims and Real Mallorca, but has had struggled to make an impact and is now looking for another club.
Rahman failed to attract from interest from Europe during the international transfer window, but is still a Chelsea player for the moment.
Middlesbrough have enquired about signing the left-back on loan from Chelsea before next week’s domestic deadline.
Neil Warnock is interested in taking the defender to Boro, but it has been claimed that Chelsea have not decided what to with Rahman.
Chelsea had a couple of continental loan moves lined up for Rahman but the deals did not happen, and he is now waiting for a chance to move to a club in the Championship.
Rahman is not part of Frank Lampard’s squad and has been training with the Under-23s over the past few weeks.
Middlesbrough are keen and it remains to be seen whether Chelsea are ready to let him move to the Championship or wait for a European club in January.