The player has been linked to Jurgen Klopp's Reds in recent days.
And now the Daily Mail claims he has asked Norwich, who are relegated to the Championship, to allow him to make the move.
The issue is Norwich wanting £20 million for the 22-year-old left back, who would be a backup at Liverpool.
The Reds are offering roughly half that sum, and both sides will have to compromise for any deal to get done.
There has also been talk of a swap deal between the two clubs, with Yasser Larouci heading to Carrow Road.
Lewis played 28 games last term and was impressive, and only has a year left on his contract.