The Frenchman has managed to survive his latest crisis at the north London club despite Arsenal winning just three of their last five league games.
Garcia, meanwhile, has transformed Roma into perennial title challengers in Serie A, competing with 30-time top-flight winners Juventus.
And former Arsenal midfielder Parlour would like to see Wenger’s compatriot take over the reins from the decorated 65-year-old manager.
Parlour was asked who he would like to see succeed Wenger. He replied: “That will be the hardest decision the club have to make. They need to have a replacement lined up.
“Klopp is having a bad time this season, but someone of his calibre is needed. He changes his tactics and has been in the Champions League before.
“Roma’s Rudi Garcia is another good manager. Wenger will have a say in who is brought in. He built the club up, won trophies and oversaw the new stadium.”