Burke is only 18 years of age and plays as a winger, and is rated as one of the most promising young players in the Championship.
The Scotland Under-19 international has already featured in the Championship for Forest.
The teenager was in action for the Reds in their FA Cup third-round tie against Championship rivals Queens Park Rangers at the City Ground on Saturday afternoon.
The youngster started the game and played for the entire 90 minutes, as Dougie Freedman's side won 1-0.
Former Forest defender Thompson was impressed with Burke’s performance and has described him as a “great prospect” on Twitter.
Burke has scored one goal and created four chances in four Championship appearances so far this season. The teenager has a pass accuracy of 75% and a shot accuracy of 33%, and has won four headers and one dribble.
Forest are 14th in the Championship table at the moment with 31 points from 25 matches, 10 points behind Ipswich Town, who are currently sixth and occupy the final playoff spot.