Pritchard, a former England Under-21 international, has made two senior appearances for Spurs.
He has scored a total of 20 goals in 100 matches on loan at Peterborough, Swindon, Brentford and West Brom.
The 23-year-old would become Championship club Norwich's third summer signing, after keeper Michael McGovern and winger Sergi Canos.
Find all the latest football transfers on our dedicated page.

A fight which started on Monday evening at a food distribution centre was initially broken up by police but later continued into the night.
Hundreds of migrants live in informal camps in the Calais port, trying to cross into Britain illegally.
French police have spent months trying to break up the camps, but the migrants say they have nowhere else to go.
The latest fight between Sudanese and Eritrean migrants was broken up for the second time once riot police were deployed.
A similar incident on Sunday left about 13 people injured.
In May authorities attempted to evacuate the migrants from camps built near the port following court rulings, but many have simply moved to different areas in the city.
Norwich City are in talks to sign Tottenham Hotspur midfielder Alex Pritchard, reports BBC Radio Norfolk.
[NEXT_CONCEPT]
Clashes between African migrants in the French port city of Calais have left more than 50 people injured.