The 31-year-old centre-back has been at Fulham since the winter window on a short-term contract and has made five Premier League appearances.
He will be out of contract in the summer and his agent has been looking to find a new club in the coming months.
Duffy has clubs in the Championship who want him but Norwich are now the favourites to sign him on a free transfer.
Norwich want an experienced head in defence next season and Duffy has emerged as the top target.
The Canaries are in talks with his representatives and they are closing in on a deal to sign him this summer.
The 31-year-old is keen on the move and Grant Hanley’s injury is likely to take him to Norwich in the coming months.
Duffy has vast experience of playing in the Championship and has clocked 132 appearances in the second tier of English football.
