The Mirror's David McDonnell reported Mourinho feels "undermined" by Woodward's failure to back him in the transfer market this summer and would have quit United if he were at another club.
Per Alex Richards of the same outlet, the Portuguese was asked whether they still had a positive relationship and replied: "Of course."
When pressed on whether there were any problems between them, he offered "no" in response.
The speculation regarding Mourinho and Woodward's relationship has intensified since United lost 3-2 to Brighton & Hove Albion on Sunday following a summer in which the former was frequently vocal in his complaints about the club's lack of transfer activity.
The coach said he has not been paying attention to reports of discord between them, though, per Marca's Chris Winterburn:
Per Samuel Luckhurst of the Manchester Evening News, Mourinho also offered a prickly response when asked about the reaction to the Brighton defeat:
Shortly after the loss, United star Paul Pogba told Sky Sports neither his nor the team's attitude going into the game was right.
Per Richards, Mourinho was asked to comment on Pogba's admission but would not: "Paul said it. He has to answer by his words. If you want any explanation about Paul’s words, you must get him and ask him."
The Red Devils will need to approach Monday's clash with Tottenham Hotspur in the right way, and the manager is anticipating "a difficult match against a team that last season finished in [the] top four."
Mourinho could be boosted by the returns of Nemanja Matic and Antonio Valencia for the game, although he revealed a decision on the pair's fitness has yet to be made: "I don't know because today is still Friday and training Saturday and Sunday, match Monday, decisions to be made Sunday. But yes, [Matic and Valencia are] training with the team. [Diogo] Dalot also training with the team for the first time this week, so in terms of medical department, they are almost free."
Their returns could help the side, and it's vital United win to avoid ceding further ground to their title rivals early in the campaign.
A victory would also ease the growing pressure on Mourinho, but defeat would only exacerbate their problems.