Forest have been busy in the summer transfer window so far as they look to build a squad able to hold their own in the Premier League.
They kicked off top flight life on Saturday with a 2-0 defeat away at Newcastle United, a game in which star signing Jesse Lingard featured for the full 90 minutes.
Work remains ongoing in the transfer market and after being rebuffed by Paris Saint-Germain man Idrissa Gueye, they have zeroed in on Kouyate, according to French outlet Foot Mercato.
The 32-year-old is an experienced Premier League campaigner, having turned out for West Ham and Crystal Palace after arriving in England in 2014 from Anderlecht.
Kouyate, a Senegal international, clocked 27 appearances in the Premier League for Crystal Palace last term.
The Eagles were keen to keep him at the club, but could not agree terms on a new contract and Kouyate is a free agent.
It remains to be seen if Nottingham Forest are successful in tempting Kouyate to the City Ground.