The 32-year-old is available as a free agent after being released by Manchester United earlier this summer.
Pulis said: “Michael hasn’t gone anywhere and it’s still a possibility. There’s still stuff happening and going on. Whether we can do a deal or not is another matter.
“I’ve always said he’s a good player and someone I think people in the club would like to have around. He’s a great professional as well and Crouchy has shown what great professionals can do for the football club.”
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Liverpool have unveiled their new home kit for next season, sticking with the hugely popular retro styling of the current shirt.
The reputation of the Premier League means it is the most popular and one of the most watched leagues in the world.