The former Newcastle attacker was impressed with the performance of the 22-year-old against Manchester United away from home at Old Trafford on Saturday.
Thauvin, who moved to the Magpies from French outfit Marseille earlier this month, started the Premier League encounter on the substitutes’ bench.
The 22-year-old came on as a substitute in the 69th minute and gave a good account of himself for the 21 or so minutes he was on the pitch.
The former Lille youngster had a pass accuracy of 67%, won one dribble and committed two fouls.
Former Tottenham and Newcastle star Waddle was following the game, and he was impressed with the performance of Thauvin against United.
“Florian Thauvin's a very cultured player, he's got a lovely left foot,” the former Tottenham winger told BBC Radio 5. “He’s got a trick, he's not quick but is great on the ball and can go past players.
“I hope we see the best of him in England. You want him in the attacking half of the field, rather than doing a full-back's job."
Newcastle have yet to win the Premier League this season, having drawn two of their three games.
Steve McClaren’s side kicked off their 2015-16 league campaign with a 2-2 draw with Southampton at St. James’ Park.
The Magpies then went down 2-0 to Swansea City away from home at the Liberty Stadium, before playing out a goalless draw with United at Old Trafford on Saturday.