Mascherano, 26, has made it clear to Liverpool that he wants a move overseas in order to be reunited with his family, with his wife refusing to move to England.
He has been linked with Inter Milan - coached by former Reds boss Rafael Benitez - but Hodgson says the player is going nowhere unless the club receive the correct amount for him or until his contract expires in 2012.
''We haven't had an offer for him. We want an offer that meets what we think is his value, and Javier is perfectly happy with this,'' Hodgson said.
''He doesn't expect the club to just let him walk out of here. He hopes that a club comes in where he could be reunited with his family, which is the major problem for him, that offers us what he is worth and we accept that.
''But he has also made it clear that he doesn't regard it as a hardship to play for Liverpool Football Club. In fact, it's the reverse. It's because of family matters that he wants to go.
''He is resigned to one of two possibilities - either a club doesn't come along and offer us his valuation, in which case he stays, or we have an offer that meets his valuation, in which case he may go.''
Meanwhile, Hodgson has confirmed he is keeping tabs on PSV's Swedish striker Ola Toivonen.
"We have discussed his name, that's true," said Hodgson. "Like all teams, we are looking at a lot of players. I do know the player and think he is a good player, but can't give you any further indication.
"That doesn't mean we are going to rush in and buy him tomorrow. But he is a player who has come up, we have watched him and we know about him."