According to a recent report in The Scottish Sun, Celtic are interested in signing Flanagan from Liverpool this summer.
Although Rodgers has not definitively said that he is looking to sign the England international from his former club this summer, the ex-Liverpool and Swansea City manager has not completely ruled out the prospect.
“I would never speak about another player,” Rodgers told The Scottish Sun. “The only time I will speak is when they come in here.
“Young Jon Flanagan is a player I know very well, but there is no update on any player, really.”
Celtic are not the only club (reportedly) interested in signing Flanagan from Liverpool in the summer transfer window.
However, The Liverpool Echo has claimed that Liverpool are not looking to sell the full-back this summer.
It has been reported that Liverpool manager Jurgen Klopp considers the defender a part of his plan for the upcoming 2016-17 campaign.