Arsenal offered just over 40 million pounds for the striker, although Liverpool have maintained that Suarez is not for sale.
Suarez, who is to have a scan on a foot injury he sustained in training, said he was prepared to take his case to the Premier League.
"I want to move to play in the Champions League and there is a club offering me that opportunity," he was quoted as saying in The Daily Telegraph. "I have told the manager that I want to leave the club.
"I am being accused of showing a lack of loyalty but last year I had the opportunity to move to a big European club and I stayed on the understanding that if we did not qualify for the Champions League the following season then I would be allowed to go.
"I gave absolutely everything last season but it was not enough to give us a top-four finish. Now all I want is that Liverpool honour our agreement."
Suarez said Liverpool manager Brendan Rodgers gave him "his word" that he would be allowed to go if Liverpool did not achieve Champions League qualification.
"Liverpool is a club with a reputation for doing things the right way, I just want them to abide by the promises made last season," he said.
"I have the club's word and we have the written contract and we are happy to take this to the Premier League for them to decide the case but I do not want it to come to that."
Suarez, who is four games into a 10-match ban for biting Chelsea's Branislav Ivanovic, will miss Wednesday's pre-season friendly against Valerenga in Norway due to the foot problem.
Liverpool open the new Premier League season with a home game against Stoke City on August 17.
(Writing by Martyn Herman; editing by Robert; Woodward/Greg Stutchbury)
