The Argentina international has already declared that he is keen to leave Anfield before the close of the summer transfer window.
Barcelona coach Pep Guardiola has expressed an interest in signing Mascherano and now Hodgson has decided to play hard-ball.
"I wouldn't want to say he has played his last game for Liverpool," Hodgson said, according to Sky Sports. "The negotiations are ongoing between the two clubs and if he had played here it might have prejudiced the transfer and I didn't wish to do that to the player.
"I am seriously hoping that in the next couple of days it will be sorted out one way or another - although I have no idea which way that will be.
"Tomorrow night was out of the question but Sunday is very much a question because I think by then I should know one way or another whether he is going to play for Liverpool this season or Barcelona."