Cook can go past Tendulkar - Pietersen
Tendulkar, with 15837 Test runs, is more than 2000 ahead of his nearest rival, Ricky Ponting - and he is not quite finished yet. Cook remains 8000 adrift, although he has regularly matched Tendulkar at the same stage of his career, leaving Pietersen no doubt the record is within his compass.
Pietersen, who is expected to return for England on Thursday in the second T20 international against New Zealand, has always freely admitted that he has little knowledge of cricket history, which will be a relief to Cook, who has enough problems to deal with in managing England's Ashes campaign without being tipped to surpass the most celebrated living batsman.
Pietersen's accolade for Cook came in the second part of a pre-recorded interview with Darren Gough on Talksport - an interview which, in protest at the English media's coverage of his controversial career, he has billed as his only major pronouncement of the summer.
"His first series was against India away and we beat India," Pietersen said of Cook. "He's done exceptionally well, his cricket just keeps getting better and better.
"For me he's the right man to lead England, he's doing a great job for us and he will continue to get better and better and break every record anyone's ever set, certainly in the English game. He's on target to go for Tendulkar's numbers, if you look at the numbers and look at his age."
Pietersen also offered glowing praise for another colleague who is tipped to have a long and fruitful England career in Joe Root - not that he was overly aware who the young Yorkshireman joining England on tour for the first time in India last winter was.
"I never knew of him, I never heard of him, because when you're on the scene and young players come you just don't," he said. "But I knew that he was going to be good when he walked out to bat in Nagpur in his first Test match."
By the time Root made his debut England were 2-1 up with one Test to play and needed to avoid defeat to win their first series in India for 28 years.
"I was batting and… we just didn't want to let India back into it at all and he walked out and - just his face walking towards me for 20 metres - I thought this kid's going to be a flipping superstar.
"It was just the confidence that he walked out to bat with in his debut Test match in India, two spinners bowling, from each end, we'd just lost a wicket or a couple of wickets and he walked out with a smile on his face, and went 'All right lad, you ok, you're playing well there.' And I was like, 'Mate! I've played 90 odd Test matches and I don't walk out like that.' But it's brilliant for English cricket, absolutely brilliant."
Pietersen, no stranger to controversy, even expressed admiration for the way Root handled himself in the wake of the Walkabout bar incident in Birmingham in the early hours of the morning when David Warner pulled off a wig Root was wearing and, literally, threw the first punch of the Ashes summer.
According to Pietersen, the affair was exaggerated by the media - a view not shared by Cricket Australia, which quickly banned Warner until the start of the Ashes series. Root was unfazed, though.
"He knew the media were going to be on him all day and he'd had a haircut - he looked sharp! I think he knows how to deal with it," Pietersen said. "I saw him that day and he couldn't believe what was being made of it, but welcome to English cricket and welcome to how the media works."
Specifically referring to Wisden's assessment of Pietersen as "arrogant, self-pitying and isolated", Gough drew attention to the fact that Pietersen's relationship with the English media is now as unhealthy as with any player since Tony Greig conspired on behalf of Kerry Packer's breakaway World Series Cricket in the 1970s.
Pietersen responded: "I've been burnt too many times and it's just a case of me now concentrating on my cricket and playing my cricket as best I can because that whole situation hurt my family too much. I get it all day every day.
"Somebody asked me yesterday, 'Can you take some constructive criticism?' I said, 'Excuse me? You're talking to somebody who has it for breakfast, lunch and dinner.' So it doesn't affect me, it's water off a duck's back now. I have absolutely no interest in it but it hurt my family and my best mates.
"You go through rocky patches in every walk of life - business, marriage, as a kid, through your teenage years. In a dressing room not everyone's going to get on and I know you had altercations in your dressing room.
"I know some other great players who I speak to in other countries when I hear the things that go on in other dressing rooms now and it happens, it's going to happen. Unfortunately it was quite a famous fall out because of what happened but, no, everything's absolutely fantastic, we showed that in India the way we got on and played well and beat India in India.
"I just want to get the best out of my talent. I just live for each day, I play each day. I go out and try new things. I've got that personality, that impatient personality, that wants to try things, wants to do things, wants to achieve things and I'll never stop trying."
Pietersen also has ambitions to follow the footballer David Beckham and his wife Victoria into the fashion industry. "These last three months that I've been injured I've had quite a bit of time on my hands to sort the business side of life out," he said. "I am heavily involved in a clothing company and a footwear company in India. I've got some different stuff, other things on the horizon that I'm negotiating, talking about and signing off."
David Hopps is the UK editor of ESPNcricinfo