Monday, Astros owner Jim Crane acknowledged the team was "actively pursuing a high-end starter" and Cole is certainly available, with the rebuilding Pirates looking to move Cole, along with Andrew McCutchen and perhaps Josh Harrison.
The New York Post also reported the trade.More news: Browns add Eliot Wolf to the rebuilt front office
Cole went 12-12 with a 4.26 ERA for the Pirates last season.
Pirates right-hander Gerrit Cole delivers a pitch during the first inning against the St. Louis Cardinals on September 23, 2017 in Pittsburgh, Pennsylvania.
Cole also contributed to Pittsburgh's 2013 postseason run, making two October starts as a rookie.More news: Meghan Markle closes social media accounts after engagement to Prince Harry
However, the right-handed hurler has slipped some in recent years. He is scheduled to become a free agent after the 2019 season.
Acquiring Cole would bolster the Astros' already stellar starting rotation, as Justin Verlander, Dallas Keuchel, Lance McCullers Jr. and Charlie Morton all are under contract for the defending World Series champions in 2018.
The Pirates aren't realistic World Series contenders this year, so any return pieces will help restock the organization as it builds toward the future.More news: Senate Vote May Be Coming on FCC Net Neutrality Rules