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Poulsen has agreed a three-year contract following his move from Juventus and the Denmark holding midfielder could perform the same role that Mascherano currently fills for the Reds.
Mascherano has told Hodgson he is keen to move to Inter Milan, managed by former Liverpool boss Rafael Benitez, but the Reds chief doesn't believe the Argentine is certain to go.
"I don't want to let Javier Mascherano go. At the moment Javier has shown no signs of going," he said on Friday.
"I work with him whenever I can. He came back fairly late from the World Cup and has been away on international duty but I suppose I've had seven or eight training sessions with him now.
"We talk about football and he has made no indication ëabout wanting a moveû since our very early meeting when he made it clear where, if possible, he would prefer to leave.
"Since then he has been getting on with his work, training properly, and as far as I am concerned he is a Liverpool player and will be until the day someone signs him - and that day does not seem to be imminent."
Hodgson is confident Poulsen will play an important part this season but stressed he did not want it to be at the expense of Mascherano, who could start against Arsenal on Sunday.
"It is not a question of Christian replacing Javier, I believe Javier is going to play for us," Hodgson said.
"We didn't take Christian to replace anyone, we took him in because we wanted to improve the size and quality of our squad.
"I am happy to have both players; we are going to have a lot of games to play this year, hopefully, and we are going to need a lot of players."
Hodgson also revealed that Spain striker Fernando Torres is in contention to feature against the Gunners at Anfield after recovering from an adductor injury suffered in the World Cup final.
Torres has missed all of Liverpool's pre-season matches but Hodgson said: "There's a chance he could play. He's made a remarkable effort to get himself fit and ready for Premiership football.
"He's worked extremely hard in the two and a half weeks he's been back. I haven't ruled him out but I haven't ruled him in either.
"His chances were rightly being played down by the sports science people. They said, quite rightly, that in an ideal world he'd have a longer preparation period.
"It's quite simply a balancing job. Do we take the risk of putting him in early or do we hold him back and put him through a more strenuous pre-season programme?
"The player's feelings also have to be taken into account, so it's a delicate mixture."
