Galatasaray president Unai Aysal has begun negotiations with Atletico counterpart Enrique Cerezo over the trio and reports suggest an agreement over the transfer fees is already in place.
"We have begun negotiations with Club Atletico de Madrid over the transfers of the footballers Diego Forlan, Jose Antonio Reyes and Tomas Ujfalusi," a statement on the club's official website read. "The public will be notified of developments."
Forlan, 32, has regularly been linked with top clubs in Spain, Italy and England in recent years, while Reyes, 27, and Ujfalusi, 33, are first-team regulars at the Vicente Calderon.
Galatasaray could also be on the verge of clinching a deal to sign Inter Milan midfielder Sulley Muntari.
Frank Schreier, the player's Italy-based agent, said: "Galatasaray has made a great offer and we are considering it. There are good chances that Muntari will play in Turkey next season."
Ghana international Muntari, 26, spent time on loan at Sunderland last season but the club decided against signing him on a permanent deal.
Galatasaray are also expected to tie up a deal for Lazio goalkeeper Fernando Muslera in the near future.