Bremen are in the market for a new full-back and Riise, who has been told he can leave Craven Cottage on a free-transfer, is one of the names on the list, according to Eichin.
"I'm talking to lots of agents and we're checking the market," he told Germany's Sky television.
"Riise is certainly an interesting player and I have always said that we're on the lookout for a left full-back.
"There have been talks, but that doesn't mean anything yet."
Bremen are looking to strengthen their squad after crashing out of the DFB-Pokal to fourth-division opponents for the third time in as many seasons last weekend.
That came off the back of the worst season in the club's recent history, bringing an end to Thomas Schaaf's 14-year reign as coach.
"We've got to keep touch with reality and work hard, taking small steps to get back to where we once were," said Eichin.
"I'd therefore like to ask for patience. You don't get that in the Bundesliga and I hope we can move into calmer waters where we can improve, but that doesn't happen overnight."