Beckham is likely to seek another loan deal in January in order for the 34-year-old to gain the match sharpness required to boost his chances of featuring at next summer's World Cup in South Africa.
But speculation is now mounting he could leave LA Galaxy sooner than expected as his relationship with the club's fans continues to sour.
The England international was continually booed in a recent friendly against Milan - his first home game since returning from Italy.
However, Galaxy are expected to demand around 13 million euros for Beckham's siganture, and Galliani admits Milan are not prepared to pay that amount.
"There's no possibility for him to come sooner," the Milan chief told reporters.
"David knows that the doors of Milanello are always open for him, his lawyers also know that.
"I hope he returns in January, but before then he won't because that's when the market reopens even though he finishes there at the end of November.”
Tottenham Hotspur, Manchester City and Chelsea, now managed by Carlo Ancelotti who brought Beckham to the San Siro in the first place, are reportedly interested in the former Manchester United midfielder.
However, Beckham has made it clear that Milan is his preferred destination.
“They [Milan] have remained in my heart and honestly I am confident again I will greet them in November,” he said.
"I hope to return to play for Milan."
