HITC Sport understands Canaries want Senegalese forward.
The 31-year-old has just returned to his parent club Trabzonspor after a six-month-loan spell with Sunderland was brought to an end.
N'Doye scored once in 15 appearances for Sunderland, who were considering making the deal permanent, but with Sam Allardyce moving onto become England boss - that possibility became less likely.
Sunderland's Dame N'Doye in action with West Brom's James Chester
A number of English clubs have now made firm enquiries but Norwich are pushing ahead to try and do a deal, after they failed in their bid to land Ross McCormack - who is joining Aston Villa from Fulham instead of them.
HITC Sport understands that N'Doye would love to move back to England, and he would be prepared to drop down to The Championship.
Norwich are hoping that Turkish outfit Trabzonspor will agree to an initial loan deal for a player they paid over £2million for when they signed him from Hull City last summer.