The England midfielder has impressed since joining the Rossoneri last month on a short-term loan deal from the Los Angeles Galaxy.

However, the 33-year-old is supposed to end his stay with Milan in March and go back to America for the new Major League Soccer season.

"We really want to keep him, but it depends on Galaxy," Galliani said.

"We will hope to do so until the last minute because in any case, hope always keeps you young.

"To lose him would be a blow, hence, we will make every sacrifice and every attempt to keep him."

Beckham, who set up Milan's opening two goals in yesterday's 3-0 triumph at Lazio, has struck twice in five Serie A starts for the Rossoneri.

His team-mates, coach and Serie A opponents have heaped praise on Beckham.

"When he joined us we expected him to do well but we didn't think he would do so well," Galliani said.

Beckham's efforts have been rewarded as the former Real Madrid and Manchester United star has been included in Milan's UEFA Cup list.

"Right now he is indispensable for us," Ancelotti said.

"He can give us a huge contribution for our important games against Werder Bremen (on February 18 and February 26)."

Should Milan fail in their attempt to make Beckham's move permanent, this will see Beckham only play two European games with the Rossoneri.

However, Galliani hopes that will not be the case.

He said: "Beckham will be able to play the first leg and the return leg against Werder Bremen and after March 8 we will see."

Beckham, for the time being, is enjoying the ride and is looking forward to the Milan derby on February 15.

"I am happy at Milan," he said.

"I have fun in every game. I am in a great team with great players.

"Now I want to play the Milan derby, which is a special game.

"I have played the Manchester and Madrid derbies, it's always very exciting to play a derby clash."

Milan host Reggina on Sunday before facing league leaders Inter Milan on February 15.