After struggling to find top form for most of 2024 following an interrupted pre-season, the four-time Demons best-and-fairest has continued being the subject of innuendo around his future.
Oliver is contracted at Melbourne until the end of 2030, but the club briefly toyed with the idea of trading him last year due to off-field issues.
But Goodwin has urged the media to "lay off him" and "let go" of the idea the 27-year-old may depart the club.
"He's a Melbourne person, through and through," Goodwin said after the Demons' two-point defeat to GWS.
"He's not going anywhere.
"He's a proud Melbourne person. We love him. We love the work that he's done, and we'll get his footy right.
"He's going to be here for a long time playing some great footy."
Oliver recaptured some of his best form by collecting a team-high 26 disposals in Melbourne's loss against the Giants on Saturday night.
After being embarrassed by Fremantle last Sunday in losing the clearance battle 47-16, Melbourne's midfield lifted early against the Giants to set-up a 27-point lead at quarter-time.
"He's working incredibly hard on his game and it's great for you (the media) to recognise that," Goodwin said of Oliver's game.
"He's getting closer to his best.
"He was pretty clean in and around the ball, you can see that dynamic nature about his game, and he's going to continue to improve.
"He's had those challenges throughout pre-season, but he's continued to find to improve and and he'll keep doing that. That's the type of person he is."
Melbourne coach Simon Goodwin was on the bench despite being hospitalised in the lead-up. (Darren England/AAP PHOTOS)
Goodwin was battling illness in the lead-up to the game, forcing him to be hospitalised to cast doubt on whether he would be available for the match.
Despite the temperature dropping to seven degrees on a cold Melbourne night, the former Adelaide champion coached from the bench.
"The next couple of days I'll be laying low, dealing with an infection," Goodwin said.
"I've been in hospital for the last three or four days so head back in (after the game) to get a little bit more treatment. It's going to be OK.
"The (assistant) coaches have been dealing with most of the stuff throughout the week; Andrew McQualter, Greg Stafford, Troy Chaplin have been amazing in pulling the program together.
"It's an infection that many people deal with in life and you've just got to make sure you get the right treatment."
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