The Daily Mail says Crouch will just have to take the word of his manager Rafa Benitez, who paid £7million to sign him from Southampton two years ago, that he still has an important role to play at the club when many believe he would be on his way if anyone would meet an asking price of £15m.
Rafa Benitez has denied any problem with Crouch and insists he will always treat him fairly.
"I don't look at the strikers in a ranking of one to four," said the Anfield boss. "What is key to me is the understanding of the strikers with the other players, their form, the other team - I use all of those factors to decide on who to play.
"It's not a question of whether one is better than the other, because they all give the team something different."
Benitez explained Crouch's omission from the squad at Sunderland.
"I was thinking about the game on Saturday," he said. "My idea is to use all the players that I have. If they are training well, and Crouch is, normally we can use them.
"We have had a conversation. But I think it was more difficult for me to explain everything when he was playing the first season and he was not scoring. I was supporting him.
"Now it is easier because everybody knows he is a good player and also that I have confidence in him. I don't take any notice of the stories. There are no problems.
"It can be difficult when you have four strikers but in a top side, if you want to fight for every trophy, you need quality.
"I understand how he feels. I try to explain my idea that I can only have 16 players on the list for games here. That is not enough when in the rest of Europe you have 18."