The England fullback still has 15 months to run on his current deal.
Lawrenson wrote in the Liverpool Echo: "Johnson will know deep down he is playing for his future even if, as is almost certain, it will involve taking a pay cut.
"He has missed a chunk of the season. So perhaps FSG are thinking 'hold on, he's been off form and injured, so let's just wait and see what happens between now and the end of the season'."
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