The 28-year-old has been in impressive form for the Toffees, helping them climb up the table to challenge for European places, and boss David Moyes had wanted to extend his stay on Merseyside.
However, the new Major League Soccer season begins on March 27 and Arena is adamant that the USA international will be back with the squad in plenty of time.
Arena said: "We're not interested. Landon will be back here on 15 March, as we have said all along."
There is one outside chance that Moyes may yet get his man and that is if the new season is delayed, with a deal still to be reached between league officials and the players' union over a new labour agreement.
The LA Galaxy boss said on the club's website: "If we didn't have a league going on we would certainly entertain the idea of allowing Landon to stay there.
"If we have a league, Landon's going to be playing for the Galaxy."
If Donovan is recalled to LA Galaxy as planned then the match with Hull at Goodison on Sunday will be his last for the Toffees.