The 45-year-old is reportedly on Arsenals shortlist of candidates alongside Carlo Ancelotti, former Barcelona boss Luis Enrique and Juventus manager Massimiliano Allegri.
Rodgers, who spent just over three years at Liverpool and nearly guided the club to the Premier League title in 2015, still has three years remaining on his contract with Celtic.
But the Scottish champions have confirmed they would allow their manager to speak with Arsenal if approached.
I think its one where there is always speculation, never more so in the game than at this time whether it is players or managers, theres always lots of speculation, Rodgers told BT Sport.
BRENDAN RODGERS' TROPHIES AT CELTIC
Scottish Premiership: 2016–17
Scottish Cup: 2016–17
Scottish League Cup: 2016–17, 2017–18
Im extremely happy and Ive got three years left on my contract after this year.
The club have been brilliant to me since I came in so I dont think so much about it to be honest.
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