Hodgson brought in defensive midfielder Poulsen, 30, from Juventus this week and many believe the transfer was made as a result of the expected departure of Mascherano to Inter or Barcelona.
However, Hodgson has dismissed those rumours and said Poulsen was simply brought in to give him another option ahead of a potentially busy season.
"It is not a question of Christian replacing Javier," he said. "I believe Javier is going to play for us. We've got a lot of games to play hopefully and we're going to need a lot of players. We didn't take him in to replace somebody - we took him in because we want him to improve the size of our squad and the quality of our squad."
Asked if Mascherano's statement that he had no problem with Liverpool as a club means there is hope he could stay, Hodgson said: "There's no point in me commenting on things Javier has said or supposedly said, because I've had seven or eight training sessions with him now and we talk about football.
"Since our very early meeting where he made it clear that if possible he would prefer to leave, he's been getting on with his work, training properly, playing properly and, as far as I'm concerned, he's a Liverpool player until the day somebody signs him, and that day does not seem to be imminent."
He added: "As far as Javier is concerned, I can quite categorically state there has been no offer from any club for him. As a result, I don't see why every day I should put his loyalty or desire to the club in doubt.
"We made it clear to him that if the offer he wanted came along we probably would not stand in his way but that offer has not come along and he is working hard to play for Liverpool.
"He is a realistic player. He is playing for Liverpool and is not looking for a move to a Spanish second division team - there are very few clubs in the world that can even consider having Javier Mascherano on their books.
"If he wants to leave he will be expecting a club of a similar stature to Liverpool to come along and at the moment they haven't so I'm presuming he is very happy to stay here."
Hodgson also confirmed Liverpool are hopeful of completing a deal for Middlesbrough goalkeeper Brad Jones.
"I haven't spoken to (managing director) Christian Purslow today because he is in London with the rest of the board but I'm hoping that transfer will take place and the sooner the better," he said.
Hodgson also said he will be giving Fernando Torres a test ahead of the Arsenal game to see whether he is sharp enough to play.
"Fernando has made a remarkable effort to get himself fit and ready for Premier League football and he has a chance," he said. "He has worked extremely hard in the two and a half weeks he has been back so I certainly don't rule him out.
"His chances were being played down by the sports science people who said in an ideal world he would have a longer preparation period. They are rightly concerned if he plays too early he could have a recurrence of a knee problem which could keep him out for longer so it is quite simply a balancing job."