Martinez, 28, is out of contract at the end of the season, though United have the option to extend his deal by another year.
“I don’t think it will be a big falling-out – because I think we have question marks over this dressing room anyway,” Keane said.
“I don’t think there’s enough characters – enough men in there – but I don’t see him as a senior player at Manchester United. I see him as a centre-half who’s making lots of mistakes.”
Former United defender Gary Neville compared the incident to comments made by Wayne Rooney when they were team-mates in 2010.
Rooney pulled out of contract talks, saying he had not received “any of the assurances I was seeking about the future squad”. Two days later he signed a five-year deal and later said staying was the best decision of his career.
“I’ve got a problem with this from a player’s perspective,” said Neville. “That is a direct attack on the players you are playing with.
“So if I were Harry Maguire or Bruno Fernandes, or any other senior player, I would be absolutely fuming with him because you’re basically saying we shouldn’t be here and we should be bringing more players in.”
United travel to Leeds United in the Premier League on Sunday.