Franklin, leading the AFL's Coleman Medal race, has been named despite leaving the field with hamstring tightness late in last Friday night's big win over Carlton.
While the Hawks conducted a brief training session at Waverley on Saturday, Franklin stood to one side, doing little more than standing still and dishing out a few handballs.
But coach Alastair Clarkson said Franklin had an earlier individual session and showed enough to suggest he should face the Giants.
"If he pulls up well from that then he'll play tomorrow," Clarkson told reporters.
"If he doesn't then we won't take a risk. We'll make that call first thing tomorrow morning.
"He did everything that we asked him to do this morning, so it will all depend on how he recovers from that, but our expectation at this point is he's going to play."
The Hawks have already lost Brent Guerra (suspension) and Shaun Burgoyne (corked thigh) and remain without skipper Luke Hodge.
But the Giants have been weakened significantly, losing Tom Scully (groin), Dylan Shiel (foot) and Luke Power (ribs) to injury and resting veteran ruckman Dean Brogan.
The Giants were thrashed by Sydney by 94 points last weekend, while the Hawks are on a four-match winning streak, all by big margins.
But Clarkson said the Hawks had been impressed by the Giants' competitive approach and were not banking on a percentage-booster.
He said Carlton's upset win over top-placed Collingwood on Friday night acted as a warning of what a side with superior desperation could achieve.
"If we do the things we've been doing the past four weeks then we'll give ourselves a great chance of winning," he said.
"But anything short of that, as we saw with the Carlton victory, their attitude and application to the contest was first class.
"If we allow the GWS side to dictate terms like that then it makes it tough for any opposition."
Clarkson said Hodge should return against the Western Bulldogs next Sunday.