Signed by the Canaries last year for an undisclosed fee, the winger went on to feature on a sporadic basis for the club in the Premier League.
In the 14 appearances that he made for Norwich, Tzolis failed to score a goal or register an assist at this level as his side were relegated to the Championship.
The Greece international emerged as a potential target for Club Brugge last month.
As per a report from Metrosport, the Belgian outfit are interested in signing Tzolis either on a loan deal or on a permanent basis.
The 20-year-old was a notable absentee from Norwich’s match-day squad for their pre-season friendly with Cambridge United last night.
The Canaries stepped up their preparations for the 2022/23 campaign by securing a 3-1 victory in this fixture.
Making reference to Tzolis, Smith has admitted that Norwich will be unable to provide him with a sufficient amount of game time next season and thus are open to the possibility of sanctioning a loan move.
Speaking to the Eastern Daily Press, Smith said: “There are a few clubs asking if they could take him on loan.
“So it is a possibility he could go out on loan.
“He is a player with lots of potential.
“Unfortunately he didn’t play a lot of minutes last season.
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“We still believe there is potential to come from him.
“But we can’t give him the amount of game time this season that he needs.
“In the long run for him and the football club we feel it is better for his development [that] he goes out on loan.
“Then he comes back full of confidence after that.”
This is a sensible stance by Norwich regarding Tzolis as his development could potentially stall if they keep him at the club this summer due to the fact that he isn’t guaranteed to play at senior level.
Whereas the winger did manage to provide four direct goal contributions against Championship opposition (AFC Bournemouth) in the League Cup last season, he could find it difficult to deliver the goods in this division on a consistent basis if he does stay at Carrow Road.
By joining a club who is willing to play him week-in, week-out, Tzolis could improve significantly as a player before returning to Norwich in 2023.
The Canaries meanwhile will be aiming to launch a push for promotion in the absence of the winger.