The account - KP Genius - poked fun at Pietersen's supposed obsession with money and his ego, and was believed to have upset the 32-year-old.
A friend of Stuart Broad - Richard Bailey - has admitted starting the account, and Broad himself has made a public statement insisting he had no involvement in the account. The account has since been closed.
But according to Cricinfo, Pietersen has contended that some of the subject matter in the story could only have come private conversations he had with Swann and Anderson.
The issue matters to Pietersen because if he is right that his team-mates were feeding information to the parody and it were to go unpunished, he would point to double-standards, having been frozen out from the England team after sending private messages to South Africa players about his then captain Andrew Strauss.
Pietersen and Flower met this week to discuss their long-term future - but he was not awarded a central contract when the list was announced on Friday. With only 10 full contracts and four incremental ones offered, however, the ECB said there was room to award another central contract for the year in due course.
More talks are planned between Pietersen, Flower, and new captain Alastair Cook, but it appears that there are still deep-rooted issues holding up any resolution, which continues to dog England's preparation for their summer fixtures and upcoming T20 World Cup.
The next test of how talks are going will be when England confirm their touring squad later this week for the Test series in India at the end of the year.