The 53-year-old heart surgeon said he had been contacted by detectives after his name and mobile telephone number were found in paperwork uncovered during their investigations into phone-hacking.
In an interview with the Mail on Sunday, Dr Khan said he felt “violated” to discover his voicemails may have been intercepted ahead of the belated inquest in 2008.
He said: “To know that someone has been listening to your private messages is awful.
“It is absolutely terrible. It feels as if you have been robbed. We live in the UK. We are supposed to have civil liberties. I feel really, really violated. I am very angry.”
Scotland Yard reopened an inquiry into phone hacking last year – codenamed Operation Weeting – amid a steady flow of new revelations about the practice of intercepting the voice messages of high-profile people.
Dr Khan said that any potential compensation he may receive would be donated to a heart unit he is setting up for children in Pakistan, which he and Diana had dreamed of building.
He said: “Diana was one of those people who didn’t just talk about things.
“She was proactive. She would go out and get it done. I think this hospital would be 10 years old by now if she was alive. She did good things because she wanted to, not because of her status. She had an inner desire. It genuinely came from within her.
“I have no doubt that Diana would have been involved in this. It wouldn’t have mattered whether we were together or not.”
The pair separated in the summer of 1997.