Ciaran Whelan and Kevin McStay believe it is imperative that the Tyrone-Kerry All-Ireland semi-final goes ahead, even if a further delay is necessary.
The game was originally scheduled for this Sunday but was postponed to Saturday 21 August after a Covid-19 outbreak in the Tyrone camp.
According to co-manager Brian Dooher, just over 50% of the Red Hand panel are currently able to train.
Tyrone have welcomed the week-long delay but Dooher also warned that it might not be enough, saying that preparations had been "brutally hindered" and that they would decide next week whether they could even fulfil the fixture.
Speaking on the RTÉ GAA podcast, former Dublin star Whelan said the GAA had to consider a further delay if that scenario seemed likely.
"Kerry strolling into a final would be counter-productive," he said.
"We've had a dull enough championship to date. It hasn’t really sparked to life and you were probably looking forward to these two games, one weekend where you might have got a bit of spice.
"It’s unfortunate from a Tyrone perspective. Fair play to them that they stood up to the plate against Monaghan and played with four lads missing (Frank Burns, Rory Brennan, Tiernan McCann and Richard Donnelly).
"But obviously it’s detrimental to their squad and their ability to field, and it looks like their ability to field the following week is in doubt as well.
"The question has to be asked, will it be pushed back a further week? We do want a semi-final. You do want that game to go ahead.
"Bouncing back from this is going to be challenging, unless they get the required time to do it.
"You wonder will they get to the point where they just decide to withdraw. But you'd like to hope that they’re given time to get back and get some level of preparation before they go into the lion's den."
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The GAA are keen to avoid a longer postponement because of the knock-on delay to the club championships in the four remaining counties, with Dublin and Mayo meeting in the other semi-final on Saturday.
However, former Roscommon manager Kevin McStay believes that the prospect of a walkover in one of the year's most high-profile games could change minds in HQ.
"It was always possible," he said of Covid affecting the schedule. "We perhaps got a bit complacent and had a sense that this was all going to work out just grand.
"Kerry's preparations are upside-down.
"The club calendar is critical until it’s not, that’s a classic planning position for the GAA.
"But they have a dilemma now. Tyrone have a strong position. The semi-finals have to go ahead. The final has to go ahead.
"Whether it’s the 11, 16 September or further into it, it’s going to get done.
"The other teams left in the competition are, at the moment, clear of the virus but that could change."
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Follow Saturday's men's and women's All-Ireland football semi-finals with our live blogs on RTÉ.ie/sport and the RTÉ News app.
Watch Dublin v Mayo live on RTÉ2 or RTÉ Player from 5pm.
Watch highlights of all the weekend's action on The Sunday Game at 9.30pm on RTÉ2.
Listen to live and exclusive national radio commentaries on RTÉ Radio 1's Saturday Sport.