The batsman has been dropped for the third Test against South Africa.
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Dr Mohammed MoosajeeSouth Africa team manager
Stewart said it was his understanding Pietersen had "apologised and would like to be involved" with England.
Discussions between Pietersen and the England and Wales Cricket Board (ECB) are still ongoing.
Speaking on BBC Radio 5 live, Surrey executive director Stewart, who played in 133 Tests for England, said: "I'm hearing he's now apologised but hasn't had any confirmation back from the ECB."
Pietersen's omission from the England squad for the final Test at Lord's came at the end of a turbulent week in which he first hinted he could retire completely from international cricket, only to back down on Saturday and commit to playing for England in all forms of the game.
However, the ECB wanted assurances by Sunday afternoon from the 32-year-old that he had not sent derogatory texts about captain Andrew Strauss.
Pietersen did not to do so by the deadline and was then dropped from the squad to face the Proteas at Lord's.
On Monday South Africa team manager Dr Mohammed Moosajee insisted: "Text messages were sent, but it was banter."
And on Tuesday England's Twenty20 captain Stuart Broad denied any involvement in a spoof Twitter account that allegedly riled Pietersen and apparently formed part of his dispute with the ECB.
A member of the public claimed on Monday to be the author of the account, which was closed earlier this month.
Jonny Bairstow has been brought in to replace Pietersen in the England squad for the final Test against South Africa, which the home side must win to retain their number one world ranking.
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And England all-rounder Tim Bresnan said on Wednesday that England "may be an even better side" without Pietersen.
"It's one of those things where a talented player is being replaced by another," said Bresnan.
"So why should we miss a certain individual because he's unavailable for selection?"
South Africa all-rounder Jacques Kallis is backing Pietersen to bounce back from this setback.
"I'm sure they'll sort it out," he said. "He's too good a player to stay out of the international scene.
"I've no doubts they'll come to an agreement and something will be sorted out. These sorts of things are going to happen throughout his career, a few things have happened. I don't think it'll affect him, I think he'll bounce back and I think he's still got a lot of cricket ahead of him."