Hernandez (quadriceps) threw a 20-pitch bullpen session Monday, Christina De Nicola of MLB.com reports.
Hernandez has made just two big-league starts this season, exiting both of them with injuries which wound up sending him to the 60-day injured list. He won't be eligible to return from his latest issue, a strained quadriceps, until early August. Whether or not he'll make it back when first eligible remains to be seen, but he's at least trending in the right direction.