"I've said I want to stay here and if I do go back then it will be a bit difficult but we'll have to wait and see what happens," Beckham told reporters after his side's 2-1 defeat by Inter Milan.
Milan have said they still hope to sign the 33-year-old full-time irrespective of the MLS deadline.
Asked if there might be an outcome in the next few days, Beckham said: "I don't know. It is out of my hands and they'll be talking in the next week or two.
"Hopefully things will go the way I want them."
"They are all huge games, they are all the biggest games in football. I'm proud to have played one in England, one in Spain and one in Italy but it would have been better to win it," he said.
"We are quite far behind, we were quite far behind before the game started and we needed to win it," he said. "But you never know, this league is up and down. There obviously a chance but it is a slim chance."
