Williams (shoulder) will throw a bullpen session Tuesday, Mike Puma of the New York Post reports.
It will be Williams' first time throwing off the mound since he was diagnosed with a right shoulder strain nearly a month ago. The reliever remains optimistic about returning to pitch before the end of the regular season. Kodai Senga has pitched well since taking over the Mets' closer role, so even if Williams is activated later this month he might not pitch in the ninth inning.