Norwich are losing goalkeeper Tim Krul to Premier League side Luton Town and want to make sure they have a replacement.
The Canaries feel that competition for Angus Gunn is needed at Carrow Road and believe that Lions shot-stopper Long is a good option.
They have now decided they want to sign the Millwall man and he is set to be allowed to leave the Den.
Long has slipped down the pecking order at Millwall and boss Gary Rowett admitted earlier this month that he could leave.
The 29-year-old is likely to welcome the chance to battle for game time at Norwich.
Long made 36 appearances in the Championship for Millwall over the course of last season and kept 12 clean sheets in the process.
He played in a league clash with Norwich in March, giving the Canaries a good chance to have a close look at his abilities.
