"His performance didn't surprise me," said Hodgson. "He is a top quality player - one of the best at his job in the world and he showed that once again today.
"It's only speculation from the mass media, if I am brutally honest. We've had no offer for Javier Mascherano.
"He is playing at Liverpool and how many clubs could he move to better or on the same level? As yet, we have not received any offers from anyone.
"There are two weeks to go (in the transfer window) and you never know. Some of these clubs, for reasons best known to themselves, like to come in with offers on August 28 or 29.
"The fact is, we want to keep him here and will keep him here unless an offer comes along which is correct. By that I mean, is in keeping with his value and one we think would be wrong for us to turn down because we have said if that offer comes in we will accept it.
"But at the moment it's not there - it's not even on the horizon."
Mascherano did pick up an injury against Arsenal, but Hodgson says the 26-year-old will play in the Europa League tie against Trabzonspor on Thursday if he is fit.
Hodgson added: "Of course I would play him on Thursday.
"He picked up an injury today, unfortunately. I hope it's not too serious, but he's got a slight tightness in his muscle, which is why he had to come off. We hope it's not a pull, but it will have to be assessed tomorrow. But why wouldn't I play him?
"He is a Liverpool player and I hope he will continue to be a Liverpool player. For me, he will always be available for selection until the day comes when he's no longer here."
"It's only speculation from the mass media, if I am brutally honest. We've had no offer for Javier Mascherano.
"He is playing at Liverpool and how many clubs could he move to better or on the same level? As yet, we have not received any offers from anyone.
"There are two weeks to go (in the transfer window) and you never know. Some of these clubs, for reasons best known to themselves, like to come in with offers on August 28 or 29.
"The fact is, we want to keep him here and will keep him here unless an offer comes along which is correct. By that I mean, is in keeping with his value and one we think would be wrong for us to turn down because we have said if that offer comes in we will accept it.
"But at the moment it's not there - it's not even on the horizon."
Mascherano did pick up an injury against Arsenal, but Hodgson says the 26-year-old will play in the Europa League tie against Trabzonspor on Thursday if he is fit.
Hodgson added: "Of course I would play him on Thursday.
"He picked up an injury today, unfortunately. I hope it's not too serious, but he's got a slight tightness in his muscle, which is why he had to come off. We hope it's not a pull, but it will have to be assessed tomorrow. But why wouldn't I play him?
"He is a Liverpool player and I hope he will continue to be a Liverpool player. For me, he will always be available for selection until the day comes when he's no longer here."