The Turkish champions have made it clear that the striker is on their list of potential signings for the summer, but insisted that he was not the only player on their radar
The 31-year-old made just five Premier League starts appearances for the Red Devils last season as Sir Alex Ferguson chose to pair Wayne Rooney with either Danny Welbeck of Javier Hernandez.
Berbatov recently posted on his Facebook page that he would leave the club for the greater good, and the Istanbul giants are keen to snap up the former Tottenham man.
"We have had discussions with Berbatov's management," Arkan told Radyspor.
"We want to have a world-class striker. Our president also wants this, but the final decision rests with the coach [Fatih Terim]. Berbatov is one of the possibilities."
Akran went on to say that the club are hoping to thrash out a deal for Felipe Melo, who spent last season on loan with them, but insisted they are not to prepared to meet Juventus' asking price for the Brazilian.
"If Melo wants to play for us, he must talk to Juventus and ask them to lower their asking price. If we cannot close the Melo deal, we have alternatives."
On Galatasaray's aspirations for the season, he said: "We have big targets, and to achieve these, you have to invest.
"We want to be successful in Europe, therefore we have to have good players in our squad. We are doing what is necessary to get big success."