Since being appointed as Sheffield Wednesday boss in 2015, Carvalhal has twice led the Owls to the Championship playoffs only for the club to fail to gain promotion to the Premier League.
The second setback came on Wednesday night as the club lost out on penalties to Huddersfield Town and according to The Mirror, Norwich are now ready to firm up their interest in the Portuguese coach.
With Alan Irvine having departed his role as temporary boss, the Canaries are eager to make a permanent appointment as soon as possible and with Carvalhal not certain to remain at Hillsborough, they want to move swiftly to take him to Carrow Road.
It has been claimed that Porto are also considering Carvalhal, who would likely be attracted to such a high-profile role in his homeland, and it leaves Norwich looking to appoint the 51-year-old before the Portuguese giants make a decision over the future of current manager Nuno Espirito Santo.
Carvalhal has won 49 of his 106 games in charge of the Yorkshire outfit.