The Spaniard made 285 appearances during nine seasons as the club's first choice shot-stopper, before linking up with former boss Rafa Benitez on a season-long loan at Napoli.
And after Reina backtracked on claims that he was forced out of the club, Rodgers has revealed he met with the 31-year-old to explain he planned to give him some competition in goal.
"It wasn't anything underhand," Rodgers told the Telegraph. "It was looking into his eye and telling him he was a very good keeper but in order to be the best he can be and for us to be the best, I need to bring in another one who would be equal number one.
"He accepted that at the time, that was something he felt was needed also.
"Obviously here at the club we then have to consider the wages, as there is a financial implication too. So it was deemed through both parties that it was best for him to move on.
"As I said, I was comfortable enough to let it happen. He wanted to go and play, you have to consider that, it is World Cup year as well. He wanted to be a number one somewhere.
"We did everything we could to support him to be the best he could be. There was no rush for me to move Pepe out but I felt he needed competition so I had to bring in someone."
Rodgers has already been impressed by new No.1 choice Simon Mignolet, who was signed for £9 million from Sunderland during the summer transfer window.
"I’d seen him over the last few years, he’s adapted to the Premier League. He is a brilliant shot-stopper," the Reds boss added.
"John Achterberg, our Dutch goalkeeping coach, has been monitoring him for years.
"You see his presence, he is good with his feet, that is important, it is one of the big things I look for in my goalkeeper.