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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The reputation of the Premier League means it is the most popular and one of the most watched leagues in the world.
Five English clubs will compete in the last sixteen of the Champions League for the first time ever as Liverpool, Manchester United, Manchester City, Chelsea and Tottenham face some difficult away matches.