The forward last spent time with Crystal Palace, signing for the club in January, but he managed just four appearances in all competitions before being released this summer.
Ameobi, 33, is best known for his time with Newcastle United, when he scored 79 goals in 397 games over a 14-year period, and he has a wealth of expense at the top level of the game.
Forest are currently lacking the in the attacking positions, with Britt Assombalonga out injured. He is the only consistent goalscoring striker the club possess, and Ameobi would be able to provide cover and competition to the likes of Jamie Paterson and Tyler Walker - who are attempting to lead the line this season.
There are no indications as to whether Ameobi will be willing to drop down to the Championship having spent so much of his career in the top flight, but there are unlikely to be many sides willing to make a move for him in the Premier League.
He would be almost guaranteed first-team football at the City Ground, and on a short-term deal, Forest could do much worse than look towards Ameobi as Dougie Freedman attempts to build a side despite FFP restrictions limiting their transfer business.