After the 4-4 draw with Aberdeen at Pittodrie last Saturday, in which the visitors lost the lead three times, Mowbray was again subject to speculation about his future.
However, ahead of the Dundee United game, he said: "Where's the foundation to that?
"I could give you a quote saying this and that, that it's humorous to me, that it's laughable.
"I'm fine. I talk to you (the media) every week; you would pick up a vibe if I wasn't.
"I understand that sometimes there's hardship to go through.
"But at this moment, if we had all of our experienced defenders we might be winning 4-0, not drawing 4-4.
"We've scored 10 goals in three games, we might be untouchable, you know.
"Let's wait and see when we get everybody up and running."
Celtic v Dundee Utd. Click here to bet.