NEW YORK -- New York Yankees ace Gerrit Cole says he thinks he could return to a major league mound in June after facing hitters for the first time since spring training.

The reigning AL Cy Young Award winner, wearing a full pinstriped uniform, threw 20 pitches to Oswaldo Cabrera and Jamai Jones before Tuesday night's game against Seattle.

Cole had thrown five bullpen sessions before the batting practice. The 33-year-old right-hander, sidelined by elbow nerve inflammation and edema, said he will have one or two more BP sessions before starting a minor league rehabilitation assignment.