Bellamy fronted the media at AAMI Park ahead of the Storm's Sunday afternoon clash with Wests Tigers, with the side looking to stop a record-extending seven-match losing streak.
Melbourne last week revealed the shock news the 66-year-old was battling an unspecified neurodegenerative disorder.
When asked for specifics about the illness, Bellamy said details would remain private.
"At the end of the day, this is private to me, and footy's what you're here for," he told reporters.
The Storm said Bellamy planned to see out this season, advised by specialists that his diagnosis wouldn't have an impact on his ability to coach the team in the immediate future.
Starting his Melbourne career back in 2003, Bellamy was asked if he intended to coach next season, recently signing a new contract through to the end of 2028.
"I don't know yet, but I'm thinking about this week," he said.
Bellamy said it hadn't changed his coaching duties so far.
The master coach said he'd been flooded with messages from the rugby league and wider community since his ailment had been made public.
"One thing that I can't believe how many messages I've got," Bellamy said.
"I was surprised how much support - I know a lot of people, but at the end of the day, the support's been unbelievable in that area.
"I really apologise, I haven't got back to any I don't think, I've been pretty busy with the footy but everyone who has sent me a message ... I really appreciate it and hopefully I'll get back to you soon."
Bellamy was at the helm when the club went through the salary cap breach scandal in 2010 when Melbourne were stripped of two premierships and unable to play for competition points that season.
With Eli Katoa and Tui Kamikamica both sidelined after brain surgery, the off-season departure of key players, his own diagnosis and their losing streak, has made it one of the toughest years to deal with.
"It has been," he said.
"We lost Paps (Ryan Papenhuyzen) and Nelson (Asofa-Solomona) before the season started, and then we've lost Eli and Tui and it's knocked our forward stocks, but it is what it is.
"We've just got to get on with what we've got and work out what the best plan is and make sure everyone applies themselves to that training and hopefully in the game."
The Storm haven't lost to West Tigers in eight matches and at home since 2018.
But banking just two wins for the season, Bellamy said his team would need to avoid another second-half fade-out to avoid another loss.
"It's obviously a bit of a switch-off of their concentration ... it's been pretty consistent, so we've had a few ideas to try and solve it, but it hasn't worked out like that yet.
"Hopefully we go a bit better this week and then go from there.
"Certainly you're aware after you lose a few games that your confidence is likely to fall and we've tried to keep it positive within themselves as individuals, but also as a team."
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