The Hoops are expecting a value of around £15million(h/t The Sun) for the Australian who has committed his future until 2023.
Rogic was part of the Hoops side that won the historic double treble under former manager Brendan Rodgers.
As far as this season is concerned, Rogic has fared well for the Scottish giants, despite suffering a setback from the injury.
The 26-year-old has scored four goals and provided six assists across all competitions.
The attacking midfielder’s importance was felt by the Park Head side over the course of the season and finding a replacement for him is quite a difficult task.
Neil Lennon seems not to have planned any contingencies for the Australian as well.
The Northern Irish manager, who is enjoying an impressive stint in the Premier League, is eyeing to team up again with Rogic for a productive season at the King Power Stadium.
Earlier, Rodgers weighed up a move for the Hoops left-back Kieran Tierney and fellow midfielder Callum McGregor.
Meanwhile, the desire to play in England’s top flight and a sumptuous deal would let Rogic have second thoughts about his future.
Lennon, the interim manager, led the Bhoys to their eighth straight league title, whilst chances of winning another domestic treble also remain high.
They are set to play the Old Firm derby this week before their Scottish Cup finals against Hearts.
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