In what would be perceived by many as something of a coup for Forest, Fofana would bring plenty of international and European experience with him.
The 24-year-old started in France's World Cup semi-final victory over Morocco in December - one of six appearances he made at the finals, including being an extra-time substitute in the final.
Fofana has also been a regular at Monaco for three-and-a-half years, aiding their push for two top-three finishes.
On top of his World Cup and Ligue 1 experience, Fofana has also helped his side to the Europa League knockouts in back-to-back seasons.
David Ornstein claims that the bid made by Forest matches the valuation placed on the player by Monaco.
The bid of €35m (£29.8m) would be the upfront cost with add-ons also to be included, meaning Fofana would become the club's record signing.
Morgan Gibbs-White's move from Wolverhampton Wanderers last year currently holds that accolade, after joining for an initial £25m.
With a fee agreed between the clubs, Forest are yet to finalise personal terms with the player though and talks are ongoing.
Ornstein states that other clubs are closely monitoring the situation, and two of those clubs could be Liverpool and Manchester United.
Liverpool have struggled all summer to find replacements for outgoing pair Fabinho and Jordan Henderson.
Moves for Moises Caicedo and Romeo Lavia have slipped through their fingers, and even though a move for Wataru Endo is set to go through, Liverpool are expected to remain in the market.
Meanwhile, Man United have been chasing Sofyan Amrabat for much of the summer, but terms have still not been agreed, so both clubs could provide competition for the French international.
Forest have been linked with a myriad of players all summer, but they have had a much quieter summer compared to last.
Manager Steve Cooper has been vocal about adding further reinforcements to their squad, especially after their opening day defeat to Arsenal.
Cooper said: "We know if we really want to grow, get better and improve in this league, we need to bring some players in. I really hope the club can do that,"
"It doesn't get any tougher than this league. We managed to survive last season. We did it in a certain way. We've got to try to evolve that, but to do that we need to add to the starting team and to the squad," the Forest manager added.
Matt Turner, Anthony Elanga and Ola Aina remain the only new faces at the City Ground, while Chris Wood had his loan move made permanent from Newcastle United.