Williams (shoulder) threw a live batting practice session Monday and will face hitters again Thursday, Anthony DiComo of MLB.com reports.
Williams does not anticipate needing a rehab assignment, so he could be activated from the 15-day injured list as soon as this weekend if things go well Thursday. He's been sidelined for a little over a month with a right shoulder strain. Kodai Senga has taken over the Mets' closer job and pitched well, so it's not a given that Williams will see save chances down the stretch if/when he's reinstated.