Rose revealed last month that, having been told there is no new deal for him at Spurs, he would refuse to be sold and would sit out the remaining 18 months of his current contract as long as Mauricio Pochettino kept picking him.
The Argentinian was fired several days later and replaced by Mourinho, but Rose says nothing has changed and there are no plans for a discussion with his new boss.
"I've never had a conversation with him and I don't see why I need to," Rose said after playing 90 minutes in Tottenham's 3-1 Champions League defeat at Bayern Munich.
"As I said before, I'm here for the next 18 months so I don't see why I need to have a conversation with the manager.
"I want to do as well as I possibly can, work as hard as I can to achieve what looked impossible a few weeks ago, and that is finishing in the top four.
"I'm looking forward to a massive Christmas run that we've got."
Rose has been notorious for his public criticism of how the club has been run, once saying he was sick of having to Google their new signings to find out about them, but he was impressed with their ability to attract Mourinho.
He hopes the Portuguese can live up to expectation and help deliver silverware to north London.
"I had the privilege of working under Mauricio for five and a half years and now, I have to be honest, I never thought I would be managed by Jose Mourinho at Tottenham," he said.
"That's credit to the club, how well they've progressed throughout the years and to get someone like Jose has been obviously brilliant.
"He's one of the most decorated managers of my lifetime so it's been a good start for the team and I've enjoyed it so far.
"I think everybody has got to start again. I think we're all starting from the same starting point, or at least I hope we are anyway. I should think I'm no different to anybody else.
"I feel very lucky to work under him. He's won a lot of trophies and we're all excited to see.
"We want to do well in this competition and, as I said, he is a serial winner so I imagine we will be looking to win the FA Cup and finishing in the top four of the league."
Rose made just his second start under Mourinho in the defeat at Bayern, where the coach tested out his fringe players in a dead rubber.
Not many shone, but Ryan Sessegnon did, scoring an impressive goal on his first start for the club having spent the majority of his first four months at the club injured.
"We know Ryan is for the future we know what he can do now, but he was just so unlucky," Rose added.
"He arrived at the club injured I think and then he had a bit of a setback but I hope there's not a lot of pressure on him and he is so down to earth, he's so quiet.
"We're all looking forward to seeing what he can do for us in the coming years.
"His goal was a brilliant finish, he helped me out as well defending.
"He's so unselfish and he was a big threat attacking as well. I'm over the moon for him and I hope that is the first of many for him."