The experienced goalkeeper has been linked with a number of clubs, but the Ligue 1 side have seemingly already taken the first stepMonaco have already approached Barcelona goalkeeper Victor Valdes over a summer transfer.
The 31-year-old will leave the Spanish champions once his contract expires at the end of the 2013-14 campaign and he recently admitted that he sees Monaco as an interesting option to continue his career.
Valdes has also been linked with a move to the Premier League, but Monaco seem determined to lure him to Ligue 1 instead.
"Monaco have already discreetly contacted Valdes a number of times," Giuly told Bein Sport.
"I have spoken about it with him and he told me that he's pleased they have contacted him. He has asked me about a number of things.
"I do not know what decision he will make in the end, but I would be happy if he joined Monaco.
"Victor is looking for a place with a little less pressure than at Barca. He has been at the club ever since he was a kid and he needs a new goal."
Giuly played alongside Valdes at Barcelona between 2004 and 2007 after joining the Catalans from Monaco.