Zenit are said to have been impressed with the Socceroos star when he played against them with the Hoops in the UEFA Europa League last year.
He still has four years left on his current contract, and Scotland's Herald report Celtic will not entertain any offers below £15 million (A$27 million) amid rumours of English Premier League interest, from Southampton and Leicester City, in the midfielder too.
The Scottish club's resolve is set to be tested, though, with Zenit reportedly preparing to make a multi-million dollar transfer bid.
Rogic is understood to prefer a move to England, but could be tempted by a lucrative Russian Premier League contract.
The 26-year-old joined Celtic from the A-League's Central Coast Mariners in 2013.
He's scored 23 goals in 101 matches for the Bhoys - winning four league titles, four Scottish cups and three league cups.
Celtic manager Neil Lennon, in his second stint at the club, signed Rogic for the club originally.