The midfielder has been training with the MLS outfit after leaving AC Milan following the expiry of his contract but any possibility of a permanent move has been ruled out
The 36-year-old is without a club after leaving AC Milan upon the expiry of his contract this summer and has been training with the MLS outfit in order to keep fit.
However, when asked whether the Dutchman's presence could lead to a permanent deal, Arena wryly replied: "Clarence is just in town looking to train a little bit. I'd be glad to sign him. And if [Lionel] Messi walks through town I would do the same."
Following his training session with the Galaxy, the four-time Champions League winner remained cagey when asked where his future lies, telling Goal.com: "I don't know."
The Los Angeles side already have the maximum of three players who exceed the league-imposed salary cap - David Beckham, Robbie Keane and Landon Donovan - so any potential move would likely involve the sale of one of that trio.
And Donovan, who recently enjoyed a loan spell with Premier League outfit Everton, hailed the Dutch midfielder's quality after seeing him up close in training.
"Even though he's not really fit, you can tell he knows how to play the game," he said. "So it's been fun for the guys and good for some of the young guys to see how he moves."
When asked by reporters if he'd like to play alongside Seedorf, Donovan joked: "Sure. Sign him up. You going to pony up [pay the money] for him?"