The Sun report that Barton has met up with Forest owner Fawaz Al-Hasawi to discuss a long-term deal.
Barton is a free agent after being released by QPR in June, and had been expected to sign with West Ham last week.
The BBC reported that the deal fell through after protests from fans of the Premier League side.
The outspoken star has not ruled out playing in the Championship, and even last week telling his Twitter followers that he has already spoken to Nottingham Forest boss Dougie Freedman.
I had a good chat with Dougie a couple of weeks ago. Top bloke. Who knows? https://t.co/T0yHqsjMiL— Joseph Barton (@Joey7Barton) August 12, 2015
Forest have had a mixed start to the season, winning four points from a possible nine in their opening three games, and going out of the Capital One Cup.
They remain under transfer embargo, which means they can only sign free agents and loan players, and are limited in terms of wages they are able to offer.
This is the biggest obstacle to a deal for Joey Barton, but if the midfielder wants to get a contract sorted, he may have to take what he is able to get.