Rodgers has been in charge of Celtic since the summer of 2016 and has a contract with the Scottish giants until until June 2021, according to Transfermarkt.com.
The former Liverpool and Swansea City manager has been hugely successful at Celtic Park already.
Under Rodgers last season, the Glasgow giants won the Scottish Premiership title, the Scottish League Cup and the Scottish Cup.
The Hoops also progressed to the group stage of the Champions League during the 2016-17 campaign, just as they have done this season.
Rodgers was successful during his managerial spell at Swansea and almost guided Liverpool to the Premier League title during the 2013-14 season.
Former Celtic striker Sutton believes that Tottenham would look at Rodgers if Pochettino leaves.
The Englishman has also suggested that Arsenal would look at the former Liverpool manager as a potential successor to Arsene Wenger.
“I disagree that Rodgers would not be considered for a top job down south as nobody there cares about Scottish football,” Sutton wrote in The Daily Record.
“Why wouldn’t he be an attractive proposition to a top English club? There aren’t too many with as good a CV as his.
“He might not go back to Liverpool but you can’t tell me Arsenal or Spurs, if Mauricio Pochettino eventually goes, wouldn’t look at Rodgers.
"It’s not a case of why would they, it’s more why wouldn’t they? He got a bit of stick at Liverpool before he left so in many ways his stock is actually rising in Scotland."