Salah featured in victory against Brighton on Saturday in his final game before he joins Egypt's Africa Cup of Nations squad.
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The striker was returning after being dropped for the Champions League win at Inter Milan for talking against manager Arne Slot and club management following last week's draw at Leeds.
Salah was seen waving to fans at the final whistle, though Sutton doesn't believe it was a final farewell.
He said on BBC Sport: "I guess everyone leaves Anfield with a questioning feeling about what happens next. Should he stay or should he leave?
"I don't think it was a farewell. There were moments where you wondered if it was a goodbye wave, but it looked more like he was applauding the fans – just like he does every week."