The Dutch great says there was often raised voices as it became more apparent the club was pushing forward without him.
"Not many times but it did happen. But with respect: no swearing or name-calling. It would happen on the field when he told me I wasn't playing. Even late on, when I was 35 or 36, he would say: 'Do you still want to come to the game? Do you want to be on the bench?' And he'd leave the decision to me. I don't know what he was thinking. Was it like 'I'd rather not have you there' or 'I've got so much respect for you?' Of course I knew when I was 35 or 36 that I couldn't play every game. But within yourself you think you can."
And you didn't want to come on for just 20 minutes?
"The arguments we had were only about those sorts of football-related things. Me playing or not playing. It was very childish, but it came from the heart – from both of us."
Adapted by Sam Wallace from 'Stillness and Speed' by Dennis Bergkamp, published by Simon & Schuster UK on September 26 at £20