Alvarez, who hasn't pitched in a game since undergoing shoulder surgery last July, threw 30 pitches in his latest bullpen, mixing his slider, fastball and changeup. As long as he bounces back from the outing without discomfort, Alvarez will move on to an extended bullpen session featuring two sets of 20 pitches Saturday.
Even then, a simulated session with hitters would likely await him before another go at a Minor League rehab stint.
Alvarez, initially expected to join the A's rotation in May, has already had to overcome two setbacks -- both occurring in rehab starts -- and only so many weeks remain for him to try to get through another and prove he's healthy enough to mount a big league mound.
That's why he would be perfectly fine making his A's debut as a reliever this season, allowing him a shortcut of sorts back into the Majors -- a stage on which he earned All-Star honors with the Marlins in 2014, when he pitched to a 2.65 ERA in 30 starts.
"Any way to get off the DL and be able to close off the season right," said Alvarez, who then hopes to log a month's worth of outings in winter ball in his native Venezuela.
Alvarez's optimism has never wavered, a trait that's been just as significant in this process as the rehab work itself.
"It's so mentally taxing, and for Henderson to come in every day with the same happy go lucky spirit, it shows a lot about his character and who he is," said Chris Bassitt, rehabbing from Tommy John surgery. "It's refreshing, and you just want so badly for him to be healthy so he can bring that to the team. For him to continually grind after setback after setback, you're hoping that he just finally breaks through and gets a shot."
The A's injured list is so long -- they have 16 players on the disabled list -- that Bassitt joked, "It's like an entire baseball team." Alvarez is one of four players who have been stuck on it all season.
"I was never prepared for this mentally at all," Bassitt said. "I did not realize how challenging it would be mentally, so having guys like him around helps. It really does, especially when the team is on the road, because we're kind of here on the lonely island."
"I've never given up," Alvarez said. "I'm here battling, and the most important thing is that I don't look back and just keep going forward."
• Shortstop Marcus Semien, who welcomed a son with wife, Tarah, on Monday, remained with his family on Tuesday and wasn't expected back Wednesday, either. Manager Bod Melvin said the club will likely place him on the paternity leave list Wednesday and bring in another player.
• Left-hander Sean Doolittle (shoulder) struck out one batter in one inning for Triple-A Nashville on Tuesday, marking his fourth rehab appearance. He'll make another with Nashville on Thursday, Melvin said.
• Catcher Josh Phegley (right knee) continues to make encouraging progress and is expected to go out on a rehab assignment soon.
Jane Lee has covered the A's for MLB.com since 2010. Follow her on Twitter @JaneMLB.