The Argentina captain (26) has two years left on his contract but wants to leave Anfield for family reasons amid reports that Inter Milan could step in.
But Hodgson said: “We want an offer that meets what we think is his value.
“Either a club doesn’t offer us his valuation, in which case he stays. Or we have an offer that meets his valuation, in which case he may go.”
After returning from the World Cup in July, Mascherano revealed that he was keen on an Anfield exit, although Hodgson remains keen to keep the combative midfielder at the club.
A reunion with ex-Reds manager Rafael Benitez, now at Inter, is believed to be the former West Ham man’s choice, but it appears any move is out of his hands.
Hodgson has yet to receive an offer for Mascherano, and added that the Argentine, whose wife has reportedly refused to move to England, remained understanding of the club’s predicament.
“He doesn’t expect the club to just let him walk out of here,” revealed the former Fulham boss, who signed defensive midfielder Christian Poulsen from Juventus earlier in August.
“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.”
The Argentine, who has two years to run on a four-year contract, has made 138 appearances for Liverpool since arriving from West Ham United in 2007. –– BBC Sport.