Reina spent last season on loan at Napoli after the Reds splashed out around £9 million on Simon Mignolet.
Following his move to the Italian side, Reina released an open letter to Reds fans which all but confirmed his career at Anfield was over.
"I am disappointed that I will not be part of [the top-four quest] and although it was not my decision to leave I will accept it just like I have always accepted any decision that Liverpool have taken for me," he wrote on his official website.
The Spanish goalkeeper also claimed that he was loaned to Napoli without being notified, and his letter could have perhaps have been seen as an affront to the Rodgers Regime.
He added: "It is only natural that I would be disappointed that the Liverpool management agreed to loan me to Napoli without telling me first, I thought that I deserved better than that even though I understand that difficult decisions have to be taken in football."
Asked about Reina's situation on the club's tour of the United States, Rodgers coldly referred back to Reina's words of 2013, and stated that was how the state of play still stood between the player and the club.
He told the Liverpool Echo: “He's back in training. Pepe made it clear last year where he is at.
"He is working well and there has been no real conversation as yet.
"He is just working hard to get fit and we will see what happens over the next few weeks.”
Reina always privately believed he was on loan for a short stay before eventually moving on to Barcelona, but the La Liga giants have since signed Marc-Andre ter Stegen and Claudio Bravo, and the 31-year-old returns to Anfield firmly behind Mignolet in the pecking order.
The Reds are unlikely to keep a high-earner such as Reina as backup to Mignolet, and the La Roja international could be asked to find a new club ahead of the close of the transfer window.
Liverpool continue their tour of the US with a game against Olympiacos on Sunday, before games against AC Milan and Manchester City, and the Reds play Borussia Dortmund at Anfield on August 10 in their final friendly of the summer.