Rose has admitted that he did discuss his future with O'Neill but remains tight-lipped on his next move.
"I have thought about my future," Rose said. "When Martin O'Neill was here, we did speak briefly.
"That has changed and it's not the time for me to go speaking to the new manager about what he wants for next season. The main priority is to have Premier League status next year.
"Once that's sorted, once we are safe, I'm sure there is a conversation to be had. I know what I want to do next year and we will just see what happens."
Sunderland face fellow relegation contenders Aston Villa in their next match on Monday evening.