Leigh Griffiths is taking an indefinite break from football to deal with what are believed to be gambling issues.
The Scotland global has scored two goals in 11 Scottish Premiership appearances for the defending champions this season and played as a substitute in last Saturday's 5-1 home win over Kilmarnock.
"Leigh will be taken out of football now for a little period of time", Rodgers told reporters.
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Celtic boss Brendan Rodgers said on Wednesday that Griffiths, 28, would be "out of football" while he gets help with "ongoing issues", including some relating to his mental health.
Rodgers added: "He's reached a point where it's a struggle for him".
The Hoops boss confirmed the Scotland global had "had ongoing issues for a number of months" but would not discuss them, instead saying they were "confidential".
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The former Hibs and Wolves hitman has been plagued with injury issues this season and has struggled for game time as the second choice striker behind club-record signing Odsonne Edouard.
Rumours have been swirling around about the reasoning behind Griffiths' absence, but the club have been keen to keep a tight lid on the matter with the striker's privacy in mind.
I thank you all sincerely and want to let you know I'm doing all I can to come back as soon as possible, a better and stronger person. We have a strong relationship but he's had number of issues outside of football. "He has all of our support - the team, the staff and the supporters".
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