The Brazilian midfielder has spent last season at the Turkish club following an unsuccessful two-year spell with Juve.
Although that deal included an option to buy the 29-year-old for £10.2 million thus summer, Gala are hopeful of taking him on a temporary basis for another season.
A brief statement on Galatasaray's website reads: "We are in negotiations with Juventus FC over a loan move for Felipe Melo de Carvalho."
Juventus, who paid Fiorentina £17.6m for Melo in 2009, won the Serie A title last season by going unbeaten in the league without the Brazilian's services.
However, at Galatasaray Melo won his first league title since moving to Europe seven years ago, scoring 10 goals in their victorious championship campaign.
"I'm very happy to be at Galatasaray," he said in a recent interview.
"I feel like I have been born again. If it were left up to me I'd sign a 10 year contract here without even blinking."