"There have been no contract negotiations," Cole told Chandler Rome of the Houston Chronicle on Friday afternoon.
An earlier report on Friday from Ken Rosenthal of The Athletic suggested Houston is engaged in contract talks with Cole and his rotation-mate Justin Verlander, both of whom are set to reach free agency after this season.
Astros owner Jim Crane confirmed the team is talking to Verlander. Cole, however, decided to "bring everyone up to speed" on his negotiations, or lack thereof in light of Friday's report.
The 28-year-old said the only discussions he's had with the Astros came when the team "asked if it would be OK to contact my representatives about an extension."
"I told them they are free to call (agent) Scott (Boras) whenever they want," Cole continued. "That was the extent of the conversation and since then, Scott has not been contacted by anyone from the club. This seems more like a phone call negotiation involving the media than anyone else."
Cole is entering his second season with the Astros, the organization that acquired him from the Pittsburgh Pirates in January 2018. He turned in a career-best year for the AL West champions in 2018, posting a 2.88 ERA and 1.03 WHIP while striking out a league-leading 12.4 batters per nine innings.
He won his salary-arbitration case before spring training, and as a result will earn $13.5 million in 2019.
While Cole might not be negotiating an extension, the Astros have been busy securing other players with long-term deals. Earlier this week the team signed reliever Ryan Pressly to a two-year extension, and on Friday Houston announced Alex Bregman's five-year, $100-million deal.