Beckham's five-year deal with the Galaxy concludes at the end of the current Major League Soccer campaign and there have been suggestions that Paris Saint-Germain and a number of English clubs are interested in signing the former Manchester United and Real Madrid midfielder.
Galaxy's owners, however, have indicated a new deal may be on offer to the 36-year-old Beckham, who has kept his intentions very close to his chest and refused to discuss his future until the end of the MLS season.
But, in an interview with the American radio station AM 570, Donovan said the Galaxy squad expected the former England captain would be around next season.
"We are all assuming that he is going to be back. I know nothing has been said, or nothing is official, but I think he loves it here, his family loves it here and he has been arguably our best player at long stretches during season.
"He looks as good now as he did even five years ago when he first came here so I think we are under the assumption he is coming back and if something changes we have to adjust accordingly," he added.
The Galaxy host the New York Red Bulls on Thursday in the second leg of their Western Conference semi-final. L.A have a 1-0 lead from the first game.
That game ended in some rancour, with a melee on the field and after the game Donovan labelled New York the "cheapest" (unsporting) team he has played against.
The U.S international said he had wanted to make his views clear after the incident where a ball thrown by Red Bulls' Mexican defender Rafa Marquez hit his leg.
"I was clearly not happy with how things ended and I wanted to make sure that people knew what was going on," he said, adding that he had not encountered such a situation before in an MLS game.
"When you have people who are disgracing or shaming the game that we are trying to build, that is really frustrating and none of us want to see that."
