Rodgers was appointed the Celtic manager in the summer of 2016, and he was in charge of the Glasgow giants until February 2019 when he left for Leicester in the Premier League.
Forrest has been on the books of the Hoops his entire professional club football career so far.
Former Liverpool manager Rodgers has raved about the 28-year-old winger, and has claimed that the Scotland international was thinking of leaving Celtic back in the summer of 2016.