The influential trio trained with Fremantle's main group on Thursday but coach Ross Lyon said they would complete more conditioning work before playing later in the pre-season competition.
Fyfe has been carefully managed through the summer after a second shoulder reconstruction sidelined him for 12 games last season. Mundy, meanwhile, suffered a minor ankle complaint late in January.
"They're available in technical terms, but we'd like to get another week of conditioning into them," Lyon said of the ball-winning pair.
"There's plenty of games for them to come, hence we get to expose some younger players."
Crowley, who suffered a torn pectoral muscle in December, will likely be available for round two of the NAB Cup after completing a short block of full training.
"He's done all the running and he's one of our elite runners – he'll probably play the week after I would think," Lyon said of the 2012 club champion.
"He's one of the elite runners of the competition so we can tick him off."
With three of its leading stoppage players sidelined, second-year midfielders Tom Sheridan and Cameron Sutcliffe could play big roles on Saturday night after strong pre-seasons.
Sutcliffe, who played four games last season, has been the standout performer among Fremantle's young midfielders this pre-season, while Sheridan's hard running has stood out.
"It's a great competition to be able to expose some young players and people who had really strong pre-seasons," Lyon said.
"Certainly Tommy Sheridan will play and Cam Sutcliffe – they've had really terrific summers.
"The ultimate aim over the next three to four weeks is to condition our players for round one and the season proper and identify what areas we're going well in and need to improve in."
Lyon said the club had just two injured players on its list, with rookie key forward Matt Taberner contracting glandular fever and Anthony Morabito having LARS surgery on his left knee.
The coach said young ruckman Zac Clarke had suffered a slight adductor tweak but would be available during the NAB Cup.
"We're just being conservative with him, we'll just hold him back one week," Lyon said.
"He's had an enormous summer. He's put on five kilos, he's 202cm and now he's up around 96-97kg."
Lyon said his second pre-season with Fremantle had involved "more work into more players at a higher quality" and he welcomed the expectations being placed on last year's semi-finalists.
"We'll focus on what we can control and we'll work really hard together and give our greatest effort," he said.
"If that leaves us short that's OK, because we know we've given great effort and we'll improve."
Nathan Schmook is a reporter for AFL Media. Follow him on Twitter: @AFL_Nathan
