Hodge faces a fitness test later in the week to decide if he is fully recovered from a lingering calf injury, which has kept him on the sidelines for the Hawks' first four matches.
"His training has certainly lifted, which gives us some encouragement," Hawthorn football operations manager Mark Evans told hawthornfc.com.au on Tuesday night.
"It's the same as the last couple of weeks though, we'll have a look at where he's at by the end of the week."
Isaac Smith (calf) and Grant Birchall (knee) will also be tested ahead of selection for the Swans clash.
Birchall was a late withdrawal from the Hawks' loss to West Coast on Saturday night after receiving a knock to the knee against Adelaide in round three.
"He did some training today," Evans said.
"He got the point of someone else's knee into the side of his knee, just below the joint.
"So it's been a little bit irritable and swollen for him underneath the knee. It's not actually in his knee."
Smith has been out since experiencing back tightness and a minor bleed in his calf after the round two loss to Geelong.
"When he last played, the real issue was tightness in the back," Evans said.
"He came out of the game and had some calf tightness as well, but we actually thought that would disappear pretty quickly.
"But that's actually been the thing that's been lingering for him.
"There was a little bit of a bleed, but it doesn't appear to be major.
"These things are usually around the one-week mark, but having said that the first game he missed was more in relation to the back and we thought the other stuff would disappear.
"We'll just have to see where he's at at the end of the week."
Luke Breust, concussed in a heavy collision with Crow Brodie Martin a fortnight ago, is available.
"He's fine," Evans said.
"He was pretty good all of last week, but we just felt that with the six-day turnaround and the flight, we'd err on the side of caution."
Mark Macgugan covers Hawks news for AFL.com.au and hawthornfc.com.au. Twitter: @AFL_MarkM.