The trio are all showing an interest in the gangly goalgetter and were under the impression he may be surplus to requirements at Anfield following the arrivals of Fernando Torres, Ryan Babel and Andriy Voronin.
However, Reds boss Rafael Benitez plans to rotate his five strikersthis season and is under no pressure to sell after already allowing Craig Bellamy to join West Ham for £7.5million.
Crouch has two years left on his current deal and Benitez believes the 26-year-old is worth in excess of the £16million Tottenham spent on Darren Bent, according to the News of the World.
Benitez rates has previously told the England international he must stay and fight for his place this season.
"The only thing I can say is that Peter Crouch will be staying with us. I have said to Crouch that he must fight for his position and he will stay with us," he said.