Media reports on Sunday morning claimed Shiels had been dismissed by Killie chairman Michael Johnstone on Saturday evening.
The Rugby Park team finished ninth in the Scottish Premier League last season, and Shiels was in trouble with the Scottish Football Association for accusations about a match official and comments directed towards Celtic Football Club.
"Today's reports are wrong," a Kilmarnock spokesman said. "We have not sacked Kenny.
"As was reported yesterday, Kenny's position is under review at present due to his failure to meet a contractual performance related target and potential breaches of contract relating to media comments and observance of Scottish FA Articles and Rules and SPL Articles and Rules.
"In successive seasons we have finished fifth, seventh and now ninth. Our home record last season was the worst for over 30 years.
"These factors, along with the well documented SFA disciplinary issues and other internal problems concerning Kenny's conduct have necessitated the review.
"The outcome will be announced next week."