The Daily Mail says City signed winger Johnson on the last day of the transfer window in January for a total fee of £8.5million, including two payments of £1m each depending on City appearances and the player being capped by England.
Johnson made his England debut as a substitute in the friendly against Mexico at Wembley on May 24.
This led to Boro immediately billing City for £1m. But there has been fractious dialogue between the clubs since because City have not paid as they insist the terms of the deal referred only to competitive England matches.
City say they will have no problems in paying Boro when Johnson plays in such a game.
They expect it to happen early next season at the start of the Euro 2012 qualifying campaign as one of the changes made to the team following the many World Cup failures in South Africa, whoever is the manager.