The 26-year old has been a strong target for West Ham United in the past few weeks but a deal could not be struck and now the Potters have put their hand up for his services.
However, Pulis admits he is not too sure if Stoke would be able to finalise a deal to bring Jarvis to the Britannia Stadium.
"I like Jarvis. There are a lot of players I like, but whether I can bring them to the football club, that is a different matter,” he said.
"Jarvis is a very, very good player that we have liked for a long time."