The England international has yet to appear for the Galaxy since ending his loan stint with Milan but Arena says it won't be long until he is back amongst the MLS action.
"My guess is he fits in there. Exactly where is to be determined," Arena said after the 1-0 win over SuperClasico rivals Chivas USA.
"We haven't had him on the field with our team yet but obviously we think the world of David. He's an outstanding player and healthier than he has been in a long time."
Beckham watched the Galaxy win from a suite with French legend Zinedine Zidane.