Newspaper reports on Wednesday claimed that Barton, who is a free agent after being released by Queens Park Rangers this summer, was in talks over a move to the City Ground.
But it is understood Barton spoke to Reds boss Dougie Freedman much earlier this summer and told him the club could not afford his wage demands.
Under Forest’s transfer embargo, they cannot spend more than £10,000 a week on wages per player.
The 32-year-old said on Twitter on Wednesday: “[I’ve] not reached any agreement with anyone. [I’ve] spoken to several [clubs]. Long way to go yet. Needs to be the right project. No more time can be wasted.”
Barton was previously in talks with West Ham after new manager Slaven Bilic held talks with the 32-year-old, but the deal fell through.
Barton, who began his career at Manchester City before joining Newcastle, was released by QPR after four years and over 100 appearances for the club.