The MLS outfit have been strongly linked with the England international ever since it became apparent that Lampard would not be offered a contract extension at Stamford Bridge.
The Galaxy have a place available in their squad for a 'designated player' following the departure of David Beckham.
Lampard has been touted as an ideal candidate to fill the void, and Arena concedes that the 34-year-old does appeal.
He has been reluctant to speculate on the likelihood of an agreement being put in place, but has fanned the transfer flames with his latest comments.
Arena said: "I wouldn't be surprised if over the next week or so we're going to have some sort of decision with a designated player.
"We wouldn't rule a move for Lampard out. It's always a possibility."