Swansea slipped into the relegation zone on the weekend with defeat to high-flyers Arsenal.
Jordi Amat played under Mauricio Pochettino at Espanyol.
The Spaniard has struggled for first-team football this season.
HITC Sport understands that the Spaniard has emerged as a late window target for Canaries boss Alex Neil.
Swansea City defender Jordi Amat has committed himself to the club until 2018.
What do Swansea City fans need to know about their club's latest addition?