The Premier League champions have been struggling for numbers in recent weeks, but Remy remains surplus to requirements at Stamford Bridge and Antonio Conte is happy for the player to leave the club.
Remy is short of match practice after several injury problems, but according to Sky Sports News, both Newcastle and Swansea are looking to sign the 30-year-old before the end of the transfer window.
During the 2013-14 campaign, Remy spent a year at Newcastle on loan, with 14 goals being scored in 26 appearances in the Premier League, and the Magpies appear to be keen on a loan deal.
However, Swansea would need to sign Remy on a permanent basis due to Premier League rules stating that clubs cannot loan more than one player from the same team, with Tammy Abraham having already been allowed to move to the Liberty Stadium.
Last season, Remy failed to score in eight appearances during a period at Crystal Palace.