Rahman joined the Blues on a £15 million move from Augsburg last season but only made 15 Premier League appearances last season.
The 21-year-old left-back would play first team football at the Yellow Canaries who are currently in pursuit of a replacement for Caner Erkin who played as a full-back for Fenerbahce last season.
The Blues are reluctant to let Rahman leave on a permanent deal considering he has another four-years remanning on his contract but could be tempted to let him leave on loan to gain experience.
Rahman would play first-team football at a side challenging for the league title and playing Champions League football were he to make the move.
It remains to be seen what plans recently appointed Chelsea boss Antonio Conte has for the Ghana international next season.