Boyata will be available on a pre-contract with his current deal at Celtic due to expire in the summer. The Belgian international has gone on to enjoy a solid year with the Parkhead side after refusing to play in their Champions League qualifier with AEK Athens following a failed move to Fulham.
Despite this, Rodgers wants the 28-year-old as a long-term replacement for Leicester stalwart Wes Morgan.
The Northern Irish boss has also identified Aston Villa midfielder John McGinn as another target.
The Scottish international almost moved to Celtic in the summer as they tried to negotiate his transfer from Hibs. But when their offers fell short of Hibs’ valuation, Villa swooped in to grab him from under their noses.