Payton said he hoped to hear something from the league by Tuesday. Otherwise, he would not expect the suspensions to start until Week 2 at the earliest.
"Generally, (the NFL is) mindful of the preparation time it takes to bring in players to replace them," Payton said. "I don't anticipate that being an issue."
Smith and Grant both practiced Monday. Payton said both looked good. They were not available when reporters were allowed in the locker room at the Saints' training headquarters.
Currently, the Saints have only two other defensive ends on the roster: Bobby McCray and Jeff Charleston. Anthony Hargrove also played end earlier in his career and began working at that spot when the Saints opened camp, but has spent most of the preseason at tackle.
If the NFL decides to enforce the suspensions soon, Payton said the Saints also could re-sign DE Paul Spicer, who started the last preseason game but was waived Saturday when the roster was trimmed to the regular-season maximum 53.
"He's someone who has gotten a lot of work," Payton said. "We'll stay in touch with him and make sure he's staying in shape."
Smith and Grant were among a handful of NFL players who tested positive last year for the banned diuretic bumetanide, which can be used to mask steroids. Others included Minnesota Vikings defensive tackles Kevin and Pat Williams (who are not related) and former Saints running back Deuce McAllister, currently a free agent. Those five remained active while appealing their suspensions, first through league channels and then in federal court in Minnesota.
The players argued their suspensions were improper because the NFL knew bumetanide had been detected in the over-the-counter StarCaps weight-loss supplement they were using, but failed to inform players when they called a league hotline to check if the supplement was permitted.
A federal judge dismissed most of the players' claims in May, but the NFL Players Association appealed. Last month, the league filed a motion seeking permission from the court to enforce the suspensions immediately instead of waiting for the appeals process, but a ruling on that motion was still pending.
McCray said he and Charleston are preparing as if they could start in case Smith and Grant are barred.
"We're going to miss those guys if anything happens," McCray said. "We don't want it to happen, but if it does, we'll have to adjust."