Already without star backman Jake Lever for up to another 10 weeks, the winless Demons could be without All-Australian defender May for a crunch clash with the Dockers on Easter Saturday.
May didn't feature in an open training session in front of fans at Casey Fields on Tuesday and was spotted hobbling around the venue off field.
Pickett was restricted to running light laps after rolling his ankle in Saturday night's loss to Essendon.
May is dealing with plantar fasciitis in his heel.
"It's Tuesday, the first session, so he (Pickett) will train fully Thursday and be right to go on the weekend," Goodwin said.
"Steven had an incident in the game with his plantar fasciitis, but in a lot of ways it's a positive incident, because it's a tear that helps the recovery.
"We're hopeful that he'll get up for Thursday and be right to go on the weekend.
"In some ways, an incident that is pretty painful at the time can be a real positive moving forward."
Goodwin added they wouldn't take a risk with May, but expected the 33-year-old to be in a defence that will need to handle red-hot Fremantle forward Josh Treacy, who is the equal leader of the Coleman Medal.
Lever suffered a major setback last week in his recovery from an ankle issue sustained against North Melbourne in round two.
"He's obviously frustrated," Goodwin said of Lever.
"He had a pretty strong pre-season in terms of getting himself prepared.
"He's clearly going to be out for eight to 10 weeks, so he's recovering."
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