Mark said: "We'd love you to come out and play on some stuff."
Ronnie replied: "I'm going to hold you to it with Amy's band, you want me to play any sessions you're going do, Mark. I'm definitely going to do that, what an honour for me to play with Amy Winehouse's band.
Mark admitted Amy - who was found dead at her London home in July - was the most talented singer he has ever worked with.
Speaking to Ronnie on his Absolute Radio show, he said: "Her voice is so good, you forget. I mean, because I've heard it so many times it kind of just like becomes so abstract. Then I listen to her sing, I'm just like 'She's the best singer I ever worked with', you know."
As well as producing 'Back to Black', Mark worked with Amy on a cover of 'Valerie' for his album 'Version' and while the single was popular, the producer told how Amy preferred an earlier version they recorded of the track.
He explained: "We recorded it, the original way we recorded it is much more of like a Curtis Mayfield soul-type record, and then we'd done eight takes of that and everyone's packing up their guitars, and at the last minute I was kind of like 'Can we just do one with like the You Can't Hurry Love beat'.
"So it was like one of those things where it was kind of like lucky that we just, as they're out the door, we cut it like that. But the original way is the way that she really loved it and it was kind of her favourite version, it's a version that I guess she always meant it."