The Brazilian international has been a regular at the Stadio Olimpico since joining from Atalanta - initially on loan - in 2020.
Ibanez was called up to the most recent Brazil squad in June, and featured all the way through Roma's run to the Europa League final last season.
Fabrizio Romano claims that a bid of €25m (£21.5m) has been submitted by Forest, who are currently short on defensive numbers.
Moussa Niakhate is currently out injured for the Premier League club, and they were thrashed 5-0 by Rennes in a friendly on Wednesday.
Joe Worrall and Scott McKenna were Steve Cooper's only available central defenders for the encounter, as Willy Boly also missed out.
Ibanez has pedigree given that he played 15 times on the way to Roma's Europa Conference League success in 2021-22.
Despite falling at the final hurdle in last season's Europa League, Ibanez once again played a central role, featuring in 13 games on Roma's road to Budapest.
Ibanez has garnered a reputation for being an extremely aggressive defender though, and was sent off in the second Derby della Capitale of the season against Lazio in March.
On top of that dismissal, Ibanez picked up 16 yellow cards last season, but his aggression does reap benefits from set pieces, as the 24-year-old has nine goals in his Roma career.
However, highly-rated Evan Ndicka has joined on a free from Eintracht Frankfurt, as well as Diego Llorente on loan from Leeds United, heightening the competition at Roma for a starting spot.
With Chris Smalling and Gianluca Mancini also among those vying for a place, Ibanez may find himself fighting hardest for a spot in the side.
However, despite reports, Ibanez's agent Lodovico Spinosi has refuted the claims, stating that Ibanez wishes to stay at Roma.
Speaking to TAG24, Spinosi said: "Ibanez is doing very well at Roma and wants to stay, he feels valued by the coach and his teammates. He is in love with the city and the fans, so he wants to continue playing in the yellow and red shirt."
After stating that no official bid has actually been made, Spinosi did confirm that should one come through, they will consider it.