It appears Swansea want Djourou to help solidify the back four as they attempt to stay in the Premier League.
Djourou is currently playing for Antalyaspor in Turkey, and it would take a decent transfer fee to get him to Swansea in the middle of the season.
Swansea coach Carlos Carvalhal is aware that he needs more bodies if he is going to mount a dramatic recovery this season.
Even though the side were creditable defensively in a 1-0 win over Liverpool, leaking goals is one of the main reasons why they are bottom of the league.
Djourou is available because of a dispute with his current employers about his pay, which means that a good bid by Swansea could facilitate a quick transfer.