"There's nothing that's been stated publicly that he's leaving," Arena said. "No one has said he's leaving. We've been consistent from the start. We have players out on loan. We expect them to be back on March 9.
Arena said the wrangling over the services of the 33-year-old player, with Milan failing to meet the Galaxy's valuation of the midfielder, had distracted him rather than his players as they prepared for the new season.
"More to me than the team," he said. "They're going on with the business of pre-season, trying to earn positions on the team and getting better. Players on loan have nothing to do with what they're doing. They haven't asked me one question.
"Where did we have Landon Donovan going 60 days ago? We had him gone as well. You simply can't worry about it.
"It is what it is. If you want to track back the last 60 days in this exercise you could fill a mental hospital."
Several players told the Galaxy website they were resigned to being without their captain until midway through the season.
"I think the best thing we can do is prepare as we have been," said midfielder Chris Klein.
"Go with the guys we have right now. That's kind of how we've looked at it the whole pre-season. We'll continue to do that and prepare for the regular season the best we can."
Midfielder Dema Kovalenko said the Galaxy players understood Beckham's wish to stay in Milan, however bad the effect would be on their own team.
"At the end of the day, the guy has to do what's best for him and what makes sense for him," Kovalenko said. "Right now we have to understand that.
"To be honest, it would be nice to have him here because he's a great player, but all we can do is get ready for the season."