Kidd worked with the Notts County boss Ince when he was a star at Old Trafford.
Ince said: "Kiddo was and still is a fantastic coach. His knowledge of football is second to none and, above all, he is a top, top person.
"At United, he was always the person you would turn to when you had just been slaughtered by the gaffer.
"Kiddo would be there to put an arm around your shoulder and he would make it feel not quite as bad as it was. That's a great trait to have.
"I can see signs of the same chemistry now. People are right when they think that Roberto Mancini is probably more methodical, straight down the line and knows what he wants as a boss.
"So, Kiddo probably gives City that balance in much the same as he did at United alongside Fergie. When you look and hear what is happening at City you sense that Mancini is one of those managers who knows what he wants, doesn't take no for an answer and knows how to get it.
"That's a sign of a top boss - just like Fergie. He took over at United in 1986 and didn't win the title until 1993, but he always knew what he wanted and it's the same with Mancini.
"I don't know how long it will take Mancini to win a title - they could do it this year.
"You'd think that, with the players they have, they will definitely win something in the next season or two - just not the FA Cup this time round!"