The midfielder and his agent are due to meet director of football Barry Fry after manager Darren Ferguson expressed interest in the 22-year-old.
Fry told the Peterborough Evening Telegraph: "Toumani is a holding midfielder who breaks up play, but he is also a good passer of the ball. We tried to sign him last summer but as Hereford were promoted with us he stayed with them.
"Darren Ferguson fancied having another go at him after Hereford's relegation last season and we have now had a bid accepted.
"I'm speaking to the player and hopefully we will reach an agreement. It's another young, hungry player who will fit in superbly with the rest of the squad.
"Darren thinks he offers something different to the other midfielders at the club."