Beckham, 36, helped Galaxy lift the MLS Cup last month with Donovan scoring the game's only goal in the final against Houston.
The Yank has now rejoined Everton on a two-month loan.
Donovan, 29, said: "The last three or four games of LA's season were the best I'd seen him play all year.
"He keeps himself in great shape. If he's asked to play in the Olympics, he'd absolutely do it."