Jai Serong and Tom McCartin are also pressing to return from injury in Friday night's Marn Grook game against the Magpies at the SCG.
Coach Dean Cox said on Wednesday for the time being he won't play four key forwards. Hayden McLean came in for Curnow last week and kicked three goals in his first senior game this season.
Joel Amartey and Logan McDonald are the other Swans key forwards.
Curnow was out with abdominal soreness last weekend, while Serong had a hamstring problem and McCartin was sidelined a fortnight ago with a knee sprain.
"So far they've done what they had to do - that's train over the weekend, the early part of the week, and just assess them now in some match play," Cox said of the trio.
Asked about their key forwards, Cox said: "I won't say 'never' play all four, (but) at the minute we won't."
Carlton are said to be interested in Amartey, who will be an unrestricted free agent at the end of the season.
"We want Joel here - he knows that, his management knows that," Cox said.
The Blues will no doubt also consider Swans performance boss John Longmire as they start the search for their next full-time senior coach.
The day after Michael Voss resigned, Cox said he had not asked Longmire whether he was interested in a return to coaching.
"He's a great coach and obviously a great football person as well - that's a decision for him to make," Cox said.
The Swans will start firm favourites against the Magpies, who will be without Darcy Cameron, Scott Pendlebury and Darcy Moore.
Not surprisingly, Cox was uninterested in any talk about a weakened Collingwood.
"They are a very experienced football team, who have played a lot of footy together," he said.
"They've always been up for the fight and always will be."
While the Magpies only managed nine goals in last week's loss to Geelong, Cox said Sydney's defence also needed improvement.
"That's what we spoke about as part of our review ... to get back to playing the defensive brand of football we know we can play," he said.
"We need to make sure our defensive intent is right from the outset, because ... the last couple of weeks it hasn't been to the level it should be."
Matt Roberts is out with a groin injury and Cox said it was clear he needed a rest.
The Marn Grook game will honour the Indigenous community as part of the Sir Doug Nicholls Round and Cox noted Sydney's rich tradition of great players, including Adam Goodes, Micky O'Loughlin and Lance Franklin.
"We've had some of the best ... hopefully (we) make them proud," Cox said.
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