Swansea are in the process of identifying a new manager as they are about to lose Russell Martin to Southampton.
Martin has given his verbal agreement to the move and it is now dependent on the two clubs working out compensation.
The Championship side are looking for a replacement and are not against the idea of bringing someone from outside England.
And it has been claimed that Garcia is a coach the Welsh side are monitoring as a potential new manager.
The 50-year-old is looking to get back to work this summer and is keen to take up a fresh challenge.
He has been out of work since being sacked by French side Reims in 2022 and is open to a move to England.
Swansea are one of several Championship clubs who are interested in the Spaniard at the moment.
Garcia has experience of managing in the Championship where he previously worked at Brighton and Watford.