The Netherlands international had reportedly been identified as a potential acquisition with United preparing for the possible departure of David De Gea to Real Madrid.
However, United signed Argentine goalkeeper Sergio Romero on a free transfer earlier this summer and the 28-year-old has subsequently started all four matches for Louis van Gaal's side this season, and Cillessen expects to stay at Amsterdam ArenA for the 2015-16 season.
"As far as I know it [interest from Manchester United] has never been a thing," he told NOS.
"I, the club, or my agent have never heard anything. As for me, this season begins and ends at Ajax."
Cillessen has made six appearances in all competitions for the Dutch giants so far this season.