South Africa-born Pietersen was sacked by England in 2014 after the ill-fated Ashes tour in Australia, during which the maverick batsman was accused of being disengaged from the team as the tourists crashed to a 5-0 defeat.
"I haven't spoken to him since that day but I think time is a great healer," Cook told BBC Radio's test match special.
"We spent a lot of time together and created some amazing memories. The thing is, we never fell out. Since then, the internet has fallen out for us.
"As two blokes, if you take cricket out of it, we have never fallen out. He will have a different opinion, I'm sure," he added of the batsman who brought the curtain down on his own playing career in March.
Cook, who will retire from international cricket after the fifth and final test against India starting on Friday, said that as captain, he was involved in the decision to sack Pietersen but the final call was collectively taken by senior ECB figures.
"I'd refute anyone saying that I was the one that chucked him down the stairs but I was involved in the decision and I believed it was right at that time," Cook added.
"Looking back, I can safely say all the decisions I made were done for the best of the England cricket team at that time. On that one, there were a lot of other people, way above my head, also involved in it."
First Published: September 7, 2018, 6:45 PM IST