Perez threw a light 15-pitch mound session during Saturday's workout and reported no issues with his shoulder, which he injuried Feb. 26 during an outing against the Royals. Perez was scheduled to go through another abbreviated bullpen session on Monday after throwing without incident.
If Perez completes Monday's step with no lingering problems, he would then likely be cleared to resume throwing full bullpen mound sessions.
Francona said Saturday's mound workout was encouraging.
"He's doing really well," Francona said. "His intensity probably exceeded what we were expecting or hoping, but he still feels really good. That's terrific."
Perez saved 39 games last season and posted a 3.59 ERA in 61 appearances, earning a spot on the American League All-Star team for the second consecutive year. Perez ranks fifth in the Majors over the past three years in saves (98) and save percentage (89.1), and signed a one-year, $7.3 million contract this winter to avoid arbitration.
Perez suffered an oblique injury in his first bullpen session of last year's Spring Training and was sidelined from Cactus League action until March 29. The closer logged only three official innings in three appearances and was cleared to join the Opening Day roster.
Right now, Cleveland's projected Opening Day bullpen includes setup man Vinnie Pestano, sidearmer Joe Smith, lefty Rich Hill and right-hander Cody Allen. Righty Matt Albers, who is out of Minor League options, is also a front-runner for a relief role. Other candidates include Bryan Shaw, Nick Hagadone, Scott Barnes, Matt Capps (non-roster invitee) and David Huff (out of options).
Francona has noted that the Indians, who play 13 games in a row with no days off to open the regular season, are weighing whether to carry seven or eight relievers on the Opening Day roster. The manager would not speculate about how Perez's status might influence the makeup of the bullpen.
"To be honest with you, I don't know yet," Francona said. "Obviously, we spend a lot of time thinking about what we want to do and we'll get there. I promise you, when we leave here, we'll have a 25-man roster. I can't give you a whole lot more than that right now."