Northern Ireland international Cathcart wants new Stoke City manager O'Neill to remain in charge of the Green and White Army into the summer if they manage to qualify for Euro 2020.
"It's between him and Stoke what he has decided but as players, we want him here for these games, in March and hopefully all the way to the Euro finals if we get there," the 30-year-old said.
Cathcart's regard for O'Neill is based on more than just the results he has achieved with Northern Ireland - he also credits the manager with improving his game.
"When Michael first came into the squad I wasn't starting here, there were good players in my position and it was difficult to get in but I never felt like I didn't want to be involved and learn more,' said Cathcart, who made his international debut in 2010 but has won the bulk of his 46 caps under O'Neill.
"Michael gave me a lot of confidence even when I wasn't in the Premier League.
"When I was at Blackpool I was in the team and he told me he wanted me to play and I learned a lot of things off him from the tactical side. He's been a big manager for me and I've learned a lot from him."