May was a late withdrawal from the Demons' season-opening defeat to GWS last week and is unavailable for the clash with North Melbourne at Marvel Stadium on Sunday.
The 33-year-old will see a specialist over the weekend to determine the next course of action.
"We'll have a bit more of an update on where it sits from there," Goodwin said on Friday.
"He's progressing really well. He's got his voice back and speaking, which is good."
Max Gawn was out of action for six weeks over summer with a similar injury, but the Demons are adamant May's setback is less serious.
"It's definitely not as bad as that," Goodwin said.
"It's probably more shorter-term than longer-term, and once we get that specialist report we'll be able to give a bit more information."
The coach made three changes to his side to face North Melbourne after forward Aidan Johnson was handed a one-match ban for a dangerous tackle.
May is joined on the sidelines by emerging midfielder Caleb Windsor, who has been hospitalised with another foot infection.
The 19-year-old missed part of the pre-season with a previous infection and pulled up sore again after round one.
"It is a bit of a setback ... he's actually been in hospital having some antibiotics," Goodwin said.
"It's all heading in the right direction and he should be out in the next day or so.
"He won't play this week, but it's very short-term and we just need to make sure we get on top of that infection."
First-round draft pick Harvey Langford is also out of the side, while Charlie Spargo is back for his first game since the start of last season after overcoming his achilles problem.
Daniel Turner and Taj Woewodwin are Melbourne's other inclusions, while North will bring in Toby Pink and Dylan Stephens for Jackson Archer (suspension) and Griffin Logue (hamstring).
Goodwin took a glass-half-full approach to his review of the last-minute defeat to the Giants, after Melbourne held the upper hand through three quarters.
He was particularly pleased with his reunited midfield group, as Christian Petracca showed glimpses of his best on return from injury.
Petracca combined well with Clayton Oliver, Jack Viney and ruckman Gawn before GWS got on top in the midfield in the decisive final term.
"To get them all back together operating well inside the centre square and around clearance is really important for us," Goodwin said.
"Like for any team, to have your best players up and running and impacting the game is significant.
"To have those guys doing what they do - and you can see where they're going to get to - is exciting for our supporters."Â
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