Hawks coach Sam Mitchell did not discount the possibility of the rival captains going head-to head on Saturday at Engie Stadium.
Apart from being two of the most important players in the match, Sicily and Greene are also among the most physical and mean-tempered players in the league.
It comes as Hawthorn continue to happily talk up how physical they expect the clash to be, with the two teams' last five games decided by 13 points or less.
Defender Blake Hardwick is the more likely match-up for Greene, who again showcased his match-winning heroics in round 24 against St Kilda.
But any time that Sicily spends on his Giants counterpart would be worth the price of admission.
"That's the great thing about sport, you don't know what's going to happen," Mitchell said before Thursday morning training.
"Obviously the two captains, whether they end up spending some time on each other, there could be some fiery (moments)."
Earlier this week, Hawks forward Dylan Moore spoke of "punch-ons" at training last weekend as they let off steam in the pre-finals bye.
That was music to Mitchell's ears.
"I saw Moorey's comments and I'd like to think we train at the more physical end of the clubs in the AFL," Mitchell said.Â
"Pleasingly, they had a few blues, but no-one got into anything too serious.
"It's a bit of fun and I'm glad they're enjoying the physicality of the game, because that's going to matter a lot on Saturday.
"For one team, the season's over.
"There's a level of physicality that's going to be there - two really good pressure teams.
"I'd expect a really heated game and who can withstand it longer ... who can stand up when it matters?"
Mitchell was asked whether it might be worth double-teaming Greene, especially if the scores are close late in the game.
"He's a very good player, isn't he? But I think if you look across their season, they've won some close games," Mitchell said.
"You could probably double-team him, you could probably double-team the other Green (Tom).
"You could probably double-team (Finn) Callaghan and assuming (Jesse) Hogan comes in, he could probably do with a couple of match-ups as well.
"So it's pretty important we play our own way and make sure we have some threats that they feel they need to double-team as well."
While Hawthorn must win four straight to claim the premiership, Mitchell said it is an open finals series.
"No-one's done it from eighth yet, so that's our little rite of passage to get in the history books," he said.
"We feel like we've been in pretty good form. We haven't got every job done, but our game has been pretty consistent at a high level - maybe not right at its premium, which it's going to have to be from now.
"We feel like we're in a season that's very, very open. Every game seems like a 50-50 to me."
He is also unconcerned that Hawthorn have a 0-8 record at the Giants' home ground.
"We've got to win there at some stage - it may as well be Saturday," he said.
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