The Ghanaian's 18-month spell with Bundesliga outfit Schalke has been an unfullfilling one and he spent more than a year out following a cruciate ligament injury sustained on international duty at the African Cup of Nations.
He has managed just four appearances for Schalke this season but has regained full fitness and Reims are aiming to take over that loan.
Rahman was signed by Chelsea from Augsburg for £21.7 million in August 2015, but he made little initial impact with just 23 appearances for the Blues, and he is not the only player who could move on from Stamford Bridge before Thursday's transfer deadline.
Winger Callum Hudson-Odoi has handed in a transfer request as he pushes for a switch away from Stamford Bridge.
"I don't know. I can't say,” Hudson-Odoi said when asked by the BBC if he will join Bayern.
“I just keep working hard and you never know what happens. I can't say [if I spoke to Bayern],” he added.
Olivier Giroud could also leave the west London club following the arrival of Gonzalo Higuain from Juventus.
And Michy Batshuayi is also expected to change loan clubs before the transfer window closes.
He has had a lack of game time on loan at Valencia, but Crystal Palace have already rejected the chance of taking the Belgium international, who shone at Borussia Dortmund last season and is now wanted by Monaco.