The Bluebirds suffered a terrible season in the Championship, finishing only five points clear of the relegation zone.
Cardiff City parted ways with Sabri Lamouchi, who took charge of the club in January and helped to keep them up.
The club hierarchy are determined to make sure that they get the right man in and they have identified Garcia as an ideal candidate.
Swansea are set to lose their manager, Russell Martin, to newly relegated Southampton and they are interested in appointing the former Reims boss.
According to the Spanish outlet Relevo, Cardiff have entered the race to convince Garcia to join them in the summer.
Cardiff are looking not to repeat last season’s struggles and believe that Garcia has the pedigree to lead the Bluebirds.
The 50-year-old has been out of work since last October after he left Reims and he might be open to taking the challenge.