The 37-year-old was Rodgers's captain during their time together at Anfield, famously coming close to winning the Premier League title in 2014, and the Ulsterman has warned his former player to make sure that he is choosing the right club for his first job in senior management.
"I was a little bit surprised when I saw it," he told reporters at Friday's presser when asked about the speculation. "If it is right then maybe Stevie feels it is the right club.
"He's always wanted to be a manager. I know from my time working closely with him at Liverpool that it was something he always wanted to do. He's lived with expectation all his life at Liverpool and as the captain of England.
"When you're starting out it's all about when you feel the time is right. It's not necessarily about the club, it's about the right club."