Steven Gerrard will be unavailable for the LA Galaxy's game on Sunday against the Houston Dynamo with a hamstring injury.
Gerrard was out of action for most of September but returned to play limited minutes in LA's previous two games.
He returned to England over the international break and was spotted doing some rehab work at Liverpool's Melwood training ground on Thursday.
Arena confirmed that Gerrard, whose contract expires after this season, was unlikely to return for the game in Texas.
"I don't expect him to be at the game Sunday," Arena told reporters. "He won't be playing on Sunday ...he'll be back next week. He has a hamstring injury."
Staying in England through Monday would allow Gerrard to attend Liverpool's game against Manchester United.
Arena also said that it "remains to be seen" if Robbie Keane can play against the Dynamo after the striker trained indoors on Thursday,
After the game in Houston, the Galaxy conclude their regular season the following week at home against FC Dallas. LA has already secured a playoff spot.