Mourinho spoke for four minutes and 19 seconds - much shorter than is normal - and said he had not read reports of a falling out between the two.
"I don't know 10% of what is written," Mourinho said.
"I'm not the right guy to answer."
When reminded that he had in the past always spoken about Woodward with respect, and asked if their relationship was still fine, he added: "Of course. No problems."
He was also asked whether reports of conflict were part of an "overreaction" to United's 3-2 defeat by Brighton in the Premier League last weekend, to which Mourinho replied: "You are pessimistic, I am not."
Bill Rice, BBC Radio Manchester reporter
Not much Jose Mourinho does is by accident, so when he turns up half an hour early for his news conference you can't help but wonder if he is responding to some of the stories written recently about Manchester United and his position as manager.
Certainly he caught the assembled journalists on the hop, with some arriving part way through and some missing the conference altogether.
Despite being keen to start early he was reluctant to discuss much - in fact he curtly answered 13 questions in just four minutes and 19 seconds, with an embargoed section for Monday's papers even shorter.
Mourinho wasn't willing to discuss Paul Pogba's comments that the attitude wasn't right in United's defeat at Brighton, or how he views the progress of centre-backs Victor Lindelof and Eric Bailly since joining the club - and his response to questions about whether there is any problem in his relationship with executive vice-chairman Ed Woodward was met with a single word answer - "no".
What else did Mourinho say?
Q: When Paul Pogba says the attitude in the team is not right, how does it make you feel that you have a brilliant player who can be exceptional one week and the next week, so inconsistent?
JM: Paul has to answer by his words. If you want any explanation about Paul's words you must get him and ask him.
Q: How do you feel about the way you are playing this season?
JM: I feel we played well against Leicester and we won. I feel we played bad against Brighton and we lost.
Q: What would you like to see against Spurs?
JM: I would like to play well and win.
Q: How do you do that?:
JM: To play well and win, don't make mistakes, play well and win. That is what we want.
Q: Have Eric Bailly and Victor Lindelof progressed the way you hoped?
JM: I don't analyse with you my players.
Q: What about Spurs - how impressed are you with them, Mauricio Pochettino and how they go about their business?
JM: I'm not going to comment.
Q: Is the match against Tottenham the right game at the right time?
JM: You have to play against 19 opponents at Old Trafford and 19 away. You have to play against everyone - I don't know when is the right time, the time is now. The fixtures were decided this way and we have to play Tottenham second match at Old Trafford before we go away, if I'm not wrong twice in a row against Burnley and Watford. This is what it is. Of course it is a difficult match, against a team that last season finished top four, so difficult match.