Pirates manager Clint Hurdle announced the news before Wednesday's game against Tampa Bay.
Cole, out since June 4, threw 83 pitches over six innings in a simulated game Monday. Discussions will take place over the next couple of days to determine how Cole's return will impact the rotation.
Also, Hurdle said left fielder Starling Marte cleared a concussion test Wednesday and was feeling "much better" one day after leaving Tuesday night's game in the fifth inning with concussion-like symptoms.
Marte was hurt after a head-first slide during a failed stolen base attempt. He made contact with Rays second baseman Sean Rodriguez on the play.
Hurdle says Marte, who has a swollen finger on his right hand, was not available for Wednesday's game.