"It's all bulls***, completely preposterous," the 80-year-old said of the rumours.
"I did some interviews over in Germany for a new film and I can only assume someone has twisted my words or got the wrong end of the stick," he continued.
"I haven't seen Sean for a couple of years, but my wife and I spoke to him on the phone on his birthday this week and he was very well.
"He was fine, in complete control of his senses and his usual self.
"This stuff about Alzheimer’s is just nonsense. I have no idea where they are getting it from."
"I know Sean was quite ill a year or so ago. But he is much better now and it was never anything to do with his mental state," the Zulu actor told the Scotland's Daily Record.
Sir Michael, who lives in Surrey, added: "It would be great to see him again but I know he rarely leaves his home in the Bahamas.
In an article which had the headline "Connery forgets his life" in German newspaper Bild am sonntage, quoted The Dark Knight star Sir Michael as saying "One must have serious concerns for him."
The report claimed the Edinburgh-born is suffering from "noticeable" memory loss and that only a select circle of close friends have access to him.
Sir Sean, the first man to play James Bond, said two years ago that he no longer had any interest in acting.
He became friends with Sir Michael when they starred together in 1975 epic The Man Who Would Be King.