The Demons were able to break through for their first win of 2025, ending a woeful 0-5 start to the season, by upstaging Fremantle at the MCG on Saturday.
May was struggling with a foot issue last week, but was declared fit to take on the Dockers.
But the 33-year-old suffered a groin strain at training and was pulled from the team on Friday.
Young defender Judd McVee is also expected to join May in the line-up, having recovered from a serious hamstring injury suffered in the pre-season.
"(May) was very close last week, it was a slight niggle to the groin, but we feel confident he's made some big progression," Demons coach Simon Goodwin said on Tuesday.
"He's huge. Personnel plays a big part, but so does method and Steven is a big driver in our team 'D' (defence).
"I thought our backs held up incredibly well. Tom McDonald did a fantastic job in leading that defensive unit, but we get Steven May hopefully this week, Judd McVee hopefully this week.
"(May's) got a few things he's got to work through, but we're positive that he'll be able to do that and get through."
Meanwhile, Brisbane's Kai Lohmann is expected to return to face St Kilda at Marvel Stadium on Saturday.
The exciting small forward hasn't played since round three, when he re-injured the ankle he had initially hurt a fortnight earlier.
Defender Bruce Reville (hamstring) will be out for up to four weeks.
Tough Lions back Brandon Starcevich has returned to skills training after suffering a round-one concussion, but given his history of head knocks has no set return-to-play time-frame.
Gold Coast veteran David Swallow could also play his first game of the season against Sydney on Sunday.
The foundation Sun has been cleared to play after recovering from a knee injury sustained in a pre-season match against the Swans in February.
Sydney key forward Logan McDonald has had another ankle setback and is sidelined indefinitely.
McDonald, who had been returning from his ankle injury via the VFL, reported soreness, and scans showed a stress reaction.
Skipper Callum Mills (foot) could return within two weeks, but Tom Papley (foot) is still four to six weeks away, while Errol Gulden (ankle) is seven to nine weeks off a return.
GWS star Jesse Hogan (calf) and veteran midfielder Stephen Coniglio (glute) are both in the frame to return against the Western Bulldogs, provided they prove their fitness.
Brent Daniels is sidelined for at least three more weeks with an abdominal injury.
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