The 36-year-old's contract with Juventus is set to run out at the end of the season and the Turin club have announced this would be his last season with them.
The Juventus legend, who has played nearly 700 games in all competitions for the Old Lady, has yet to decide if he will retire from football next year.
Now Galliani has admitted he would consider taking him in if he decides to play on.
"Is it never too late? I have learned to define players as talented or mediocre, not young or old," he told Sky Sport Italia. "I always prefer a talent to a youngster.
"After all, many of our stars like Paolo Maldini and Billy Costacurta retired at 40. Pippo Inzaghi is 38 and still playing for us."
Galliani also revealed that Milan had tried to sign Del Piero from Padova in 1993 just before he made the switch to Turin where he has been playing for Juventus since.
"We nearly signed Del Piero in 1993 and failing to do that remains one of the great regrets of my career," admitted the 67-year-old.
"The fact remains that before he went to Juve, Milan were interested in the player."