But the Swans remain extremely wary of a Hawks outfit they still rate as the team to beat in 2014.
A top two finish is always vital to those right in the premiership hunt, as it guarantees a home qualifying final and the best possible shot at hosting a preliminary final and finding a way into the last Saturday in September.
But with interstate clubs the Swans, Fremantle and Port Adelaide in the mix this year, that top-two finish is taking on even greater importance.
"It's a massive advantage if you can finish top two," Swans defender Nick Smith said on Thursday.
"Mind you, we're focused on this week. What happens in subsequent weeks will look after itself.
"But we really want to come out and play our best footy on Saturday night."
The Swans recorded a solid victory over the Hawks back in round eight at ANZ Stadium, but the Hawthorn side that night was missing Luke Hodge and Sam Mitchell, amongst others.
Both will be back at the MCG on Saturday night, and while Hawthorn has drifted behind the Swans in premiership betting, Smith still rates the defending premiers extremely highly.
"Yeah, I'd say so," Smith said when asked if the Hawks are still the team to beat this year.
"There's still some really good teams in the competition – them, Freo, Port.
"It is hard to do well all year when you do have injuries and they've coped pretty well and are still a really good side."
The Swans are hopeful of having some big inclusions of their own when the teams are announced later on Thursday, with Kurt Tippett (knee) and Rhyce Shaw (ankle) pushing for recalls.
Both trained with the main group before media was turned away from the session, although Dan Hannebery (ankle) seems little chance of returning this week, as he only did limited drills and no running.
A win on Saturday would be the Swans’ 13th straight and set a new benchmark in the long history of the football club.
But Smith insists the streak hasn't rated a mention.
"After we lost to North (Melbourne back in round four) and we were 1-3, it was a bit of 'jeez, what's going on here?'" Smith said.
"You don't really contemplate winning the next 12.
"We've just got on a roll and we have improved as well.
"It's not about the streak, it's about this Saturday night, and we just want to keep winning."
The match will also herald Lance Franklin's first match against his old side in Melbourne, in front of the fans that worshipped him for nine seasons.
Franklin managed 2.7 in the first game against his old club, but has hit form since then to find himself right in the hunt for a third Coleman Medal.
Port's Jay Schulz leads the way with 52 goals, ahead of Tom Hawkins (48) and Franklin (47), and Smith expects his new teammate to relish strutting his stuff in front of what's expected to be a big MCG crowd.
"He'll be looking forward to playing them," Smith said.
"I know he'll be pumped up, he loves playing on the big stage, a big crowd at the MCG, so no doubt he's looking forward to it."
