The Seasiders look ready to spend in excess of £1m for the 27-year-old, who struggled to establish himself at London Road last season.
Posh director of football Barry Fry told the Peterborough Evening Telegraph: "I am close to selling Tyrone. A Championship club are very, very interested judging by the number of times they have contacted me.
"We expect to get over £1m for him, which would be great business for the club."
Barnett previously rejected a move to Blackpool earlier in his career before he completed his move to Peterborough.