The Alex skipper is out of contract in the summer but Thordarson is desperate to hold onto his services.
"The situation with Julien is straight forward," the Icelander told the club's official website.
"He has been offered a contract in the States, an attractive contract, and now we have to sit down and see what we can do about it.
"I am keen to keep him, he has done well for us now.
"It would be sad to see him leave."