Poulsen was presented to the media yesterday after signing a three-year contract following his 4.5m move from Juventus.
The arrival of the Danish defensive midfielder was thought likely to prompt the departure of Mascherano who has been linked with a reunion with former Reds boss Rafael Benitez at Inter Milan but Hodgson said that was not the case.
Mascherano said this week he was not unhappy with the club, but wanted a new challenge in a different country but his manager stressed an exit was not imminent.
That situation may change, however, now Inter striker Mario Balotelli has completed his move to Manchester City as the Italian club may have the wherewithal to sign Mascherano.
"I don't want to let Javier Mascherano go. At the moment Javier has shown no signs of going," he said.
Hodgson said the Argentina captain was in contention for tomorrow's Barclays Premier League opener at home to Arsenal and could well start, considering Poulsen only arrived on Thursday.
The 62-year-old said the Denmark international would play an important part this season but stressed he did not want it to be at the expense of Mascherano.