Gio Gonzalez playing catch on Monday. (Alex Brandon/Associated Press)

Gio Gonzalez, who has been on the disabled list since May 18 with left shoulder inflammation, is scheduled to throw a bullpen session Thursday, according to Nationals Manager Matt Williams. That session, however, depends on how Gonzalez feels after playing catch at Wednesday.

Gonzalez has been playing catch for several days, gradually increasing the distance ahead of a bullpen session. Thursday would be his first bullpen session since landing on the disabled list.

Gonzalez threw from 120 feet during a flat-ground throwing session on Tuesday. On Wednesday, Williams said Gonzalez “pushed it a little bit harder.”

After the bullpen session, Gonzalez would throw a simulated game at a later date, Williams said. A rehab start could also be possible before a return to the rotation. But Williams offered no further details beyond the simulated game.

Gonzalez won’t be eligible to come off the disabled list until June 2, but it doesn’t appear he would be not be ready by then.