The Rossoneri have identified the current youth team coach as their No.1 candidate to replace incumbent Clarence Seedorf, who has fallen out of favour with the club hierarchy over recent weeks.
Reports circulated in Italy that certain senior Milan players had attempted to woo Inzaghi into taking the role after attending a Primavera game earlier in the spring, but Montolivo insists the suggestions are nonsense.
"There are some who made a conspiracy out of it when I and some of my team-mates went to see a game at Milanello coached by Pippo," the Italy international is quoted as saying by Tuttosport.
"We had lunch at Milanello and we wanted to provide support for the Primavera, who share our dressing room. So no, no conspiracy.
"The rest will be discussed later, as and when things are certain.
"Would I like to be coached by Inzaghi? I don't know him, in the sense I've never been coached by him."
Montolivo, who is set to be part of Cesare Prandelli's World Cup plans this summer, has backed team-mate Mario Balotelli to take the tournament in Brazil by storm.
"Balotelli is very calm. He knows this could be his World Cup, an important test for him at international level," he said.
"He knows the team is on his side, but he must make himself available to the team.
"Our common dream is to get to the final," he added. "We have to chase this dream and exceed the expectations.
"It's a tough World Cup with many strong sides - some even stronger than us - but, as I said earlier, we are strong as well and if we play as a team we create problems for everybody."