The Swans much vaunted midfield had their colours lowered by Hawthorn last Friday, when their 12-game winning was ended.
"We need to make sure that pressure in that midfield is probably a bit tighter than what it was in last week's game," Longmire said on Monday.
Hannebery would help in that area, as he was in red-hot form prior to suffering an ankle injury that has sidelined him for five matches.
"Daniel Hannebery won't play, he's probably looking OK for next week, but he might be a bit short this week," Longmire said.
He was more optimistic about veteran defender Rhyce Shaw, who he said is a chance to return after missing the past four matches with a similar, albeit slightly less severe ankle injury than Hannebery's.
"He ran well and did skills today, so we expect him to train on Wednesday," Longmire said.
"If he gets through training on Wednesday, he'll put his hand up to play."
Longmire hinted Adam Goodes could saddle up for a 17th season, after the 34-year-old, 343-game club record holder kicked a season-best four goals against Hawthorn.
"I've had a bit of a chat with him about it," Longmire said.
"It's really about making sure we focus on our team performance from week-to-week, but he says he's feeling pretty good at the moment and enjoying his footy.
"He's certainly contributing every week so he'd have to be a chance, I guess.
"He says he's feeling mentally and physically really good, so that's a good sign."
Longmire wasn't concerned about the six-day turnaround from a torrid clash with the Hawks to an SCG scrap with improving Essendon.
He pointed out they flogged Carlton by 71 points earlier this month following their last six-day turnaround after a physically taxing game in Perth.
Victory over Hawthorn would have put the Swans two wins clear of third, but they now only lead the Hawks and Geelong on percentage, with Fremantle and Port Adelaide just four points further back.
"It didn't matter previously that we had a good run of games, because straight away we're back to scrapping," Longmire said.
"That's what the ladder position is in reality, but we don't get too focused on that, because what we do know is our destiny is in our own control."
