May was taken to hospital after a collision with Hawthorn's Mabior Chol in  round two left him with two fractured ribs and a small transverse process fracture - a type of spinal injury.
The two-time All-Australian backman has already been ruled out of Saturday night's blockbuster against Port Adelaide.
Hawthorn's Mabior Chol landed on top of Demon defender Steven May after a marking contest. (James Ross/AAP PHOTOS)
But he showed positive signs as he ran laps and took part in non-contact drills during a training session at Casey Fields on Wednesday.
Goodwin confirmed May will fly to South Australia as part of an expanded Demons travelling party for the clashes with the Power and Crows at Adelaide Oval.
"We're really hopeful that he'll play the following week against Adelaide," Goodwin said.
"He's tough ... anyone that's had a crack in their ribs will understand that they are painful.
"Sneezing, coughing, laughing - all those things can cause you a fair bit of grief.
"But once you can tolerate the pain they are things that lots of players have played with previously.
"We certainly won't be silly in that space. We'll make sure that he's right, he's feeling good, he's feeling healthy and he's able to play and perform."
Fellow star defender Jake Lever spent most of the second half against Hawthorn nursing an injured right knee, but he has been cleared of major damage.
Melbourne defender Jake Lever receives some attention to his injured knee. (James Ross/AAP PHOTOS)
He took part in some training on Wednesday as he pushes to be cleared to take on Port Adelaide.
"That's exciting for our club after the weekend, where there was a bit of doom and gloom about having our two key defensive pillars out," Goodwin said.
"We're really confident (Lever) will play."
Goodwin has a headache as he searches for ways to blunt Port Adelaide key forwards Charlie Dixon, Todd Marshall and Jeremy Finlayson.
Versatile tall Harrison Petty could be thrown into defence to cover May's absence, while Adam Tomlinson and Marty Hore could also fill the void.
"We've got some options in the back half of the ground, and Harrison's one of those players that you'd love two of - one at either end of the ground," Goodwin said.
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