The controversial Uruguay forward has made clear his desire to leave Anfield in a series of interviews over the summer and the consequent speculation over his future has been intense.
Real Madrid have regularly been linked with the player, valued at at least £40million by Liverpool, but the only positive move to date in the saga has been a rejected £30million bid from Arsenal.
Arsene Wenger was asked about Suarez at a press conference in Indonesia and said: "Suarez? As you know the transfer period demands secrets and confidentiality, so I can't answer the question."
Liverpool have a strong hand when it comes to Suarez having agreed a four-year contract with him only last August.
Rodgers told talkSPORT: "Over the course of the last few months and towards the end of the season there has been a lot of speculation with Luis. But the fact is it remains the same - we value the player. He had a terrific season for us last year and showed his qualities.
"Since then I've been in communication with him through texts and conversations on the phone and it (the situation) is pretty much the same. He is a valued player. He is an absolute magician on the field.
"Luis is a real competitor, a real winner. He wants Liverpool to do so well but, like every player, every manager, and more importantly every football club, they want to be working at the very highest level.
"At the minute he is on a break, he is relaxing with his family.
"We are in constant communication. He has got three years left on his contract, we don't want to sell him, and we hope everything will be fine for the summer.
"We want to bring in few more players to reinforce the group and we think we can put up a real fight next season."