It comes as coach Wayne Bennett revealed Euan Aitken had lost four kilograms battling a virus, but could return against Canterbury next week.
Graham could join second-rower Aitken on the field against the Bulldogs, but diminutive Jye Gray will replace the tall right winger against the Eels on Saturday night.
"We'll match the big guy with the big guy," Souths coach Wayne Bennett joked.
"(Graham) has got a bit of a strain. It's not too serious."
Graham's injury history is among the most extensive of active NRL players.
The 27-year-old has been troubled by calf issues throughout 2026, having been restricted to 11 games last year with back and calf problems.
His withdrawal from the Eels game is a frustrating blow for Souths, who have been one of the NRL's most injury-affected teams this season.
They had looked set to face the Eels with close to a full-strength side given the returns of Cam Murray (calf), Tallis Duncan (hamstring) and David Fifita (suspension).
"They're quality players, they've all got great reputations and we're looking forward to having them back," Bennett said.
Bennett remains unsure whether star player Latrell Mitchell will feature again in 2026, with the superstar centre remaining a week-to-week proposition.
Mitchell has not played since Magic Round and is battling nerve damage detected in his recovery from back and calf issues.
"He doesn't know and I don't know (when he will return)," Bennett said.
"There's a good chance that may be the case (he won't play again this year), it may not either."
The outlook appears rosier for Aitken, who left the round-19 defeat of Newcastle struggling for breath.
Aitken had been battling a virus ahead of the Knights game and underwent an ECG at the stadium, though he managed to play Souths' following two games.
But after the virus sidelined him from last week's loss to Cronulla, Aitken returned to the club on Friday to complete light running work.
He has permission from Bennett to integrate fast food into his diet to regain weight.
"He can go where he likes (to eat)," Bennett said.
"He'll probably be back next week but he's lost four kilograms and he's had a pretty heavy virus that's knocked him around a fair bit."
Seventh on the ladder to begin the weekend, the Rabbitohs hold their finals fate in their own hands, likely needing to win at least three of their remaining five games to qualify.
"We've got to win some games but it's not a position that we have to win every week," Bennett said.
"The teams around us are playing some pretty tough opposition as well so I think we can probably lose one or two games."
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