Hodgson started with Mascherano in midfield for his side's Barclays Premier League opener against Arsenal despite the Argentina captain's stated desire to leave.
The 26-year-old produced a committed display and set up a goal for David Ngog before leaving the action at Anfield - which ended in a 1-1 draw - after 79 minutes with a minor injury.
Hodgson said of his performance: "It doesn't surprise me. I have had two weeks working with him and he is an outstanding player.
"He is a top-quality player, one of the best at his job in the world and he showed that once again today."
Mascherano wants to leave for personal reasons and Hodgson will not stand in his way - but only if the right offer is received.
The former West Ham player has been linked with European champions Inter Milan but, as yet, no approaches have been made.
Hodgson is hoping the situation remains that way in the closing weeks of the summer transfer window.
Hodgson said: "Let's be frank, he is playing at Liverpool, which is a good club. How many clubs can he move to which will be better or even at the same level?
"We are not looking at clubs for Javier Mascherano that go into the tens - we are looking at clubs in the single figures.
"As yet we have not received any offers.
"The fact is we want to keep him here and we will keep him here unless an offer comes in that is correct, ie commensurate with his value and one we feel would be wrong for us to turn down because we have said if that offer comes in we will accept it.
"At the moment it is not there, not on the horizon."