The Sunday Mirror reports that the Merseyside club are wary of taking risks over his future.
Rodgers has two years left on his current contract with Liverpool.
Reports suggest that Rodgers has admirers at Manchester City, Arsenal and Tottenham.
Rodgers won the Premier League Manager of the month for August.
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Summer 2016 is set to be a very exciting time for football fans, as this is when the long awaited Euro 2016 tournament kicks off.
Since Guus Hiddink arrived at the helm, Chelsea have improved considerably after a tricky start to the campaign.