Beckham, who plays for LA Galaxy in the US, had two loan spells at San Siro before being seriously injured in his most recent tenure.

The 35-year-old was present in Milan's 1-1 pre-season draw with Arsenal, but Allegri ruled out the option of re-signing him.

"I don't think so. He is now recovering from a very bad injury and at that age I think it is very difficult to come back," said the Italian.

"But it has been a great pleasure to see him here."