According to ESPN.com's Cameron Wolfe, Mularkey called the presence of the reports "ridiculous" and said he hadn't received a vote of confidence from the Titans organization: "I haven't had any support to say I was. I just assumed the worst."
NFL Network's Ian Rapoport reported prior to Saturday's game that Mularkey's job wasn't safe, and a loss may have led to his firing.
Mularkey was especially upset with the rumors because of the impact they had on his family: "I don't think it's fair to my family. When it has an effect on my family, it has an effect on me. So it had a big effect on me."
The Titans trailed by 18 points at halftime of Saturday's contest, but they scored 19 unanswered points and shut out the Chiefs in the second half.
Mularkey has spent parts of three seasons as Tennessee's head coach. After going 2-7 on an interim basis in 2015, he has posted consecutive 9-7 campaigns, including the Titans' first playoff appearance since 2008 this season.