Manchester United failed to produce a deal that would have persuaded Paul to stay at the club.
£300,000-a-week was offered to the Frenchman to stay with the club.
The club was bluffing in a new Amazon Prime documentary.
When his contract ends this month, he is expected to return to his old club.
In the documentary, which is to be released on Friday, Pogba discusses his future with his former agent Mino Raiola.
"My thought process is to show that Manchester made a mistake in waiting to give me a contract, and to show other clubs that Manchester made a mistake in not giving me a contract," he said.
The French player is filmed saying the club were bluffing when they offered him a more lucrative deal.
How can you tell a player that you want him and that you're not going to give him anything? It was the first time I've ever seen that.
After joining the United academy as a 16-year-old, he was allowed to leave the club on a free transfer and join the Bianconeri.
He returned to United for a world record fee of £89m in August of 2016 after winning four titles with the Italian club. He was part of the team that helped France win the World Cup.
There was a strained relationship between the manager and the player.
Raiola told him to try to be as good as he is with the French team.
You are different with them. Do you know what I mean? You're a member of the team. It's not what you'd expect.
With the France team, you're the real Paul Pogba, the one everyone loves. There is something blocking you.
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