Swans scouts have been spotted in attendance at the City Ground this month as the 17-year-old has enhanced his reputation as a prolific youth level marksman at first-team level.
Brereton has a host of top Premier League sides interested in him, with recent reports claiming Liverpool, Manchester United, Tottenham and Chelsea are all keen.
Described as 'level-headed' by team-mates, Brereton has just been called up to the England Under-19 squad and has a big future in the game.
Swansea's interest is probably long term and Paul Clement won't be pinning his hopes on the starlet next season unless his career progresses very quickly over the next few months.
Brereton should put pen to paper on a new Forest deal when he turns 18 next month.
He has scored three Championship goals in nine appearances this term after 17 goals in 21 games for the Forest Under-23 side.