Riise has been allowed by the Cottagers to leave on a free transfer this summer.
Eichin has revealed that preliminary talks over a transfer have been held.
Eichin said: “I’m talking to lots of agents and we’re checking the market.
“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.”
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Liverpool have unveiled their new home kit for next season, sticking with the hugely popular retro styling of the current shirt.
The reputation of the Premier League means it is the most popular and one of the most watched leagues in the world.