If all goes well, there's a possibility that Beckett will be able to return to the rotation by Thursday at the earliest, although Francona suggested the weekend was a more likely scenario.
Beckett, who has been throwing while wearing a brace, had said he experienced little discomfort on Saturday, when he threw on flat ground, and was hopeful of continuing his progression. Monday's side session, assuming the ankle doesn't flare up afterward, should be the last step to returning to the rotation.
The Red Sox are currently in a stretch in which their starters have failed to go more than five innings in eight of their last 10 games. That includes the outing by Beckett last Monday, when he was forced to leave in the fourth after experiencing pain.
Meanwhile, Clay Buchholz (back) had another good throwing session from flat ground on Sunday, throwing from 120 feet. Francona said the plan is for Buchholz to repeat that routine on Tuesday.
Third baseman Kevin Youkilis (hip, sports hernia) is expected to rejoin the club Tuesday, but Francona said it was unknown whether he'll be able to play.
Gordon Edes covers the Red Sox for ESPNBoston.com.