Sorensen, 35, spent a year as second choice before deposing Asmir Begovic and Pulis is keen to hang on to him.
"It's important we try to get something sorted," said the Stoke boss. "The club feels it's important and I feel it's important.
"Thomas has been a big part of what we have been doing at this football club over the last four years.
"During the time he was out of the Premier League team, his attitude has been fantastic. He has shown a great commitment by the way he has handled that situation.
"We have a good dressing room here and he is one of the reasons for that."