Jose Enrique insists he will fight for his Liverpool future despite being told he can leave the club.
Enrique, along with strikers Mario Balotelli and Fabio Borini and midfielder Lucas Leiva, will be allowed to leave Anfield if the Reds receive a suitable offer.
The left-back, who is entering the final season of his contract at Liverpool, suggested that he, Borini and Balotelli have effectively been frozen out by Rodgers.
The Liverpool manager has brought in seven senior players this summer to reshape his squad following last season's failure to qualify for the Champions League.
Enrique, brought to Liverpool from Newcastle for £7 million in 2011, has been unable to regain his place after struggling with a knee problem that flared up in 2013.
He played just four times for the Reds in the Premier League last season, and has not been selected since January.
He told Marca: "I'm in a difficult situation. They have pushed aside Balotelli, Borini and myself.
"I have a year left on my contract, and I guess the club would want to get some money, but I still want to stay and to fight for a place as I have always done.
"If a good opportunity comes up, with more years of contract, and more chances to play, I would look at it."
He added: "I am not going to give up. In football things can change overnight. I know that from experience.
"My knee is perfect, after two years of problems, and Liverpool must include me in the squad.
"Also, in the squad there's just one natural left-back [Alberto Moreno] and I know that if I stay, I am going to play. I want to show that some people have been wrong about me."
Enrique, 29, suggested that any move away from Liverpool would be a step down unless he went to Real Madrid or Barcelona, and he said that he had rejected a move back to his native Spain.
He added: "What I believe is that I'm not going to play at a better team than this. The only ones better are Madrid or Barca.
"Liverpool are at the same level as Manchester United. It's true that the league has not been won for many years, but you can't forget the club has won five European Cups.
"I had a very good opportunity to return to Spain, but it is difficult as the financial situation is very different than here.
"The only teams that can afford what is paid in England are the two big clubs [Real Madrid and Barcelona], so I am delighted to remain here [in England] until my legs give up."
ESPN FC's Spain correspondent, Dermot Corrigan, contributed to this report.