Petrie has suffered wretched luck with injury in 2010, breaking his left foot during the pre-season before breaking his right foot during his return game against Fremantle in round 10.
He was initially expected to miss six weeks but Swallow said the North vice-captain would attempt to prove his fitness to face the Swans at training this week.
"It'll be really good to have him back. Looking at where he is at the moment and seeing him running around today, he looks like he's not far off," Swallow said on Tuesday.
"It'd be great to have him back. He's only played the one game this year, so to have him running around in our forward line will definitely make a huge difference to our team and structure."
Sunday's game at the SCG looms as a crucial clash for both sides, who both boast a 7-7 record after 14 rounds.
The Swans have already defeated the Roos twice this year - once in the NAB Challenge and a 40-point loss in round four - but Swallow said his side was keen to turn the tables and continue its push for a finals berth.
To do so, he said North needed to eliminate the errors that cost it dearly during a 35-point loss to Geelong at Skilled Stadium last weekend.
"Whether it's your positioning in the structure at a stoppage or conforming to what the team's expectations are, if you go away from them it just can really open you up and we saw that a couple of times," he said.
"When you're playing the best team in Geelong down there, they can really hurt you on the turnover. We're just trying to eliminate those and if we can do that… we'll get better as a team."
Despite tasting defeat against the Cats, Swallow said the performance was a step forward after North Melbourne suffered heavy losses earlier in the season to top-four contenders St Kilda, Collingwood, Fremantle and the Western Bulldogs.
"We really wanted to try to rectify that. We knew earlier in the year we'd been pretty poor against some top opposition so it was just trying to bridge that gap and we'll be looking to do that in the second half of the year," he said.
"I think we've got a lot of improvement left in our group. It's only our first year under Brad Scott, so we're still learning the game plan and hopefully we can continue to improve."
