The NRL heavyweights clash on Thursday night at AAMI Park with the hosts coming off a second-round bye while the Panthers suffered a shock 38-32 loss to the unheralded Sydney Roosters.
Melbourne are looking to make amends for last year's 14-6 grand final loss, when they badly missed the presence of the banned giant prop.
Completing his five-game suspension, Asofa-Solomona turned out for Sunshine Coast Falcons in the Queensland Cup on the weekend, but was put on report for a hip-drop tackle which could see him again miss taking on Penrith.
Halfback Jahrome Hughes said it would be disappointing for Asofa-Solomona and the Storm if he was unable to play, with the forward to learn if he's charged on Tuesday.
"It'd be a bit of a blow if he can't play in this match," said Hughes, who will line up for his 150th Storm game.
"We're hoping we get him for this week - he deserves to be there, he's done a lot of hard work in the pre-season and he's still burning from missing out on last year's GF (grand final) so he's really hungry to get back on the team."
Hughes said he was excited to see Asofa-Solomona team up with new front-row recruit Stefano Utoikamanu to lay a platform for the attack.
"I'm very excited actually, very promising to have those two boys in our team and I guess someone like myself, I would love to see the go-forward to get good play-the-balls and make my job a little bit easier."
While Melbourne started the season with a 58-18 pile-on against Parramatta, the Panthers were uncharacteristically poor in their Roosters loss.
But Dally M Medallist Hughes said the Tricolours hadn't done them any favours."We can't bank on Penrith having another off game, we know that they're going to turn up, they've been turning up for many years now so we're just trying to focus on ourselves and how we turn up on Thursday night," the 30-year-old said.
"They don't have many bad games in a row so I think they're going to be up for this week's game.
"It's probably a good thing, we want to test ourselves against the best and they're the best at the moment so we're looking forward to the challenge."
Superstar fullback Dylan Edwards will miss the trip to Melbourne with a groin strain, while Penrith have a new halves pairing with youngster Jack Cole wearing No.6 after Jahrome Luai switched to Wests Tigers.
But Hughes said the depth at the Panthers, who are gunning for their fifth successive title, meant they remained a premiership force.
"They're such a quality club as a whole - they've lost players in the last four or five years and they've still been able to finish on top," he said.
"We know they're going to come out and play good footy like they have been, and I don't think it really matters too much about who's in those spots.
"They still going to be a hard team to defend and a hard team to play."
