The Canaries have opened talks with Kop chiefs for the Welsh winger, who dazzled on loan at Hull last season.
Wilson, 21, will be with Jurgen Klopp’s side for pre-season games and tours.
But Norwich hope they can convince Anfield bosses to send him to Carrow Road after that as a replacement for midfielder Maddison, who has joined Leicester.
Norwich are signing Ben Marshall from Wolves for £1.5million and want Sheffield Wednesday striker Jordan Rhodes on loan.
Wilson has been capped four times for Wales since making his debut in 2013, and has netted once for the Dragons.
After joining the Tigers on loan in January, Wilson chalked up seven goals in 13 Championship games, as well as providing four assists.
While Liverpool are believed to be interested in signing Sporting Gijon goalkeeper Daniel Martin.
The 19-year-old has been identified as a long-term replacement for Loris Karius.
Klopp could loan him him out or keep him at the club should he choose to offload former Huddersfield loanee Danny Ward.
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