The Celtic Park board have reportedly made the Northern Irishman their number one target to replace Ronny Deila.
Rodgers formerly managed Watford, Reading and Swansea before coming within a couple of matches of winning the title with Liverpool in 2013/14.
It was previously thought that Rodgers was heading back to Swansea, though the Welsh side ended their search for a long-term successor to Gary Monk when they gave Francesco Guidolin a two-year deal.
He has been high on the list of preferred candidates for Celtic, along with Roy Keane and David Moyes.
When asked last month about the possibility of succeeding Ronny Deila, Rodgers refused to rule it out, calling Celtic a “great club”.
Though a Celtic supporter in his youth, Rodgers has some concerns over the quality of football in Scotland and how much money he’d receive in the transfer market for an assault on the Champions League group stages.
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