Pietersen has refused to give any assurances over his Test career beyond the match at Lord's, having talked about "obstacles" that needed to be overcome in order for him to continue after the drawn second match of the series at Headingley earlier this week. But Botham would like to see the matter sorted out ahead of the final clash with the Proteas.
"Those sort of things should be dealt with in private between the people involved, not in the open in the run-up to a huge Test match," Botham wrote in his column in the Daily Mirror.
"It reflects poorly on the team, poorly on the game and poorly on everyone involved. It must be sorted out like grown-ups."
Botham added: "They should not be airing their dirty linen in public."
But Angus Porter, chief executive of the Professional Cricketers' Association, believes Pietersen may not be able to solve his differences with the ECB.
"I can't see any immediate prospect of a rapprochement. He's likely to play next week but it becomes an issue with the next contracts in September," Porter told the Independent.
With Pietersen and many other international players drawn by the riches of the Indian Premier League, Porter believes the status of Test cricket within the game continues to be eroded.
"The primacy of Test cricket is well-intended but the practicalities are that the trend does not support that," he said.