The 28-year-old has made just two Premier League appearances for the Canaries this season, amounting to 13 minutes of total playing time.
It is understood the Northern Irishman is desperate to be playing regular first team football ahead of next summer's European Championships in France.
Leeds boss Steve Evans confirmed his club's interest.
"He's done terrifically well for Northern Ireland and I have placed a call in to [Norwich boss] Alex Neil to see what the situation is," Evans told BBC Radio Leeds.
"Kyle needs to be playing."