Reina has failed to impress at Anfield since Rodgers took over as manager at the club.
The Sunday Mirror reports that Rodgers has given Reina until January to show he can fit into the new Liverpool.
Reina has been a key player for the Reds since joining the club from Villarreal for £6million in 2005.
But the Spaniard has made a disappointing start to the season.
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The start of the 2017-18 Premier League season is just around the corner and is shaping up to be one of the most competitive yet.
As always it is the so called “big clubs” that have splashed the most cash in the transfer window so far this summer. Manchester United or City? Arsenal or Tottenham? Who are the winners and losers of the transfer window so far?