Chairman Huw Jenkins admits he has been frustrated in the transfer market over players' wage demands, but is hoping to bring in a striker before Saturday.
"I would like to say we'd have someone in by then, but I don't know at the moment," he said.
"It could be loan or permanent, wait and see.
"There's no doubt that apart from what happened on Tuesday, our intentions were always to strengthen in a few key areas like up front.
"We will try and continue the search. We are close but it's still going to take time to sort."
Jenkins has distanced himself from speculation linking Southampton striker Grzegorz Rasiak and Norwich midfielder Wes Hoolahan to the Swans.
There was better news on the injury front, though, with midfielder Bodde resuming full training, while fellow midfielder Allen and defender Bessone are due back in training next week.
Bodde has been out of action since last November when he suffered cruciate knee ligament damage and Allen has been out since picking up a hamstring injury in the opening-day defeat at Leicester.
Pratley is recovering well from a shoulder operation, while winger Butler is expected back from a hernia operation in a few weeks.
Dobbie's rib injury is not as serious as first thought after receiving a boot from Scunthorpe's Josh Wright but is receiving pain medication.
Idrizaj is set to train on Thursday following his knee injury, which almost forced Tuesday's game to be abandoned as Swansea would have been left with six players on the pitch.
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