Ryan Bennett is set for a spell on the sidelines with a calf injury.
The Swansea City defender was withdrawn midway through his side's 4-1 defeat to Huddersfield Town at The John Smith's Stadium and subsequently missed the 1-0 triumph over Coventry City at the Liberty Stadium.
And the centre-back is expected to be unavailable for a fortnight as a result of the issue he sustained against the Terriers.
"Benno is out for a couple of weeks with a calf injury," said Steve Cooper.
The Swans are also assessing Kyle Naughton after he was withdrawn during the triumph over Coventry, although captain Matt Grimes is available after managing to play for the duration against the Sky Blues, despite suffering a shoulder problem in the first half.
"Kyle, not too sure. Fingers crossed it's nothing too serious," added Cooper.
"He played on with it for a while. We don't know to be honest. There's nothing very obvious to the physio, that's for sure.
"Grimesy is fine. I know he went down, and I was a bit worried for him but he's absolutely fine now.
"I think he had a bang to his shoulder. I guess it was a knock that he shook off.
"He played well tonight [against Coventry] by the way. I thought he was excellent. He did both sides of the game really well."
Brandon Cooper has resumed training at Fairwood following a spell on the sidelines with an ankle injury, although the clash with Nigel Pearson's side will come too soon for the Wales Under-21 international.
Wayne Routledge (calf), Jordan Morris (ACL), Steven Benda (ankle) and Tivonge Rushesha (ACL) are all unavailable.
As for the Robins, former Swan Alfie Mawson, Andreas Weimann, Callum O’Dowda, Jay Dasilva, Cameron Pring, George Nurse, Tommy Rowe, Chris Martin, Nathan Baker and Hakeeb Adelakun are all out.
Liam Walsh featured for the club's under-23s on Tuesday, although he is unlikely to be involved as he continues to step up his recovery from a quad injury.
Famara Diedhiou will be assessed after taking a knock in his side's 3-1 win over Middlesbrough while Henri Lansbury is expected to return after an Achilles issue.
Swansea City v Bristol City gets under way at 3pm on Saturday.
