The Argentina midfielder returned for pre-season training on Monday after being given an extended break following his involvement at the World Cup finals.
Hodgson had previously admitted that he had been unable to contact the 26-year-old whilst on holiday, casting heavy doubts over whether he would stay at Anfield this season.
The Reds boss met with Mascherano and the player's agent Walter Tamer to discuss his future and widespread reports claim the tough-tackling anchor man has expressed a wish to leave.
Inter Milan, now coached by former Liverpool manager Rafa Benitez, have been heavily linked with a £25million bid for Mascherano before the transfer window closes.
His representative Tamer has previously suggested a move to the European champions would be a 'dream' for Mascherano.
Any departure for Mascherano would leave Hodgson in need of a replacement and reports have claimed Sulley Muntari could be included in part exchange.
West Ham United's influential midfielder Scott Parker has also been mooted as a potential target for Hodgson, who is keen to bolster his squad.
Mascherano joined Liverpool from the Hammers in January 2007 after just six months at Upton Park and he has made almost 140 appearances during his time on Merseyside.