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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Chelsea have struggled to build momentum in the opening stages of the campaign and are currently looking over their shoulders at the relegation zone.
Who of Europe’s top strikers will move to England this summer?