Liverpool manager Rodgers left Mignolet out of Sunday's Premier League clash with Manchester United at Old Trafford after the Belgian had come in for criticism for a string of below-par performances.
Brad Jones was called into the side as a replacement for the game - which Liverpool lost 3-0 - and afterwards Rodgers admitted that Mignolet will be left out "indefinitely".
And former England international Green says some time out of the side could work in Mignolet's favour.
"How do you define indefinitely? It's indeterminate - maybe he'll be back sooner than you'd expect," he told Sky Sports.
"At some point keepers need a time out - it's strange keeping him for the Champions League and removing him straight afterwards when he didn't do a lot wrong, but that's the manager's decision.
"Simon will work hard and come back stronger.
"Clearly he's got the ability and clearly the manager believes in him - he signed him - but when times are tough the manager may take stock behind the scenes and say 'now's the time to give him a rest'.
"It's happened to me, it's happened to every goalkeeper."
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