Cruz has made progress throughout the week and will likely be a game-time decision.
"We’ll take it day by day," coach Ben McAdoo said Friday.
Undrafted rookie Roger Lewis will see a greatly increased role if Cruz is unable to play.
The Giants have other injury concerns. Starting linebacker Jonathan Casillas was a late addition to this week's injury report. He is questionable with a calf injury.
Starting left guard Justin Pugh (knee) was officially listed as out, while defensive end Kerry Wynn (concussion) and safety Andrew Adams (shoulder) are questionable. Wynn and Adams are expected to play.
Cruz didn’t practice Thursday and Friday. After spending Thursday inside, he was out on a side field Friday working with a trainer when he did light running.
The Giants didn't practice Saturday, but if they had, Cruz wouldn't have participated. Their third-leading receiver kept open the possibility earlier this week of being ready for Monday night but admitted there was a real possibility he could miss the prime-time matchup.
Cruz has a low-grade ankle sprain suffered on a 46-yard reception Sunday against the Philadelphia Eagles. He stayed in the game for the remainder of that second-quarter drive before leaving for an X-ray that came back negative. He still did not return.
With the Giants playing on Monday night, the extra day of rest could be the difference.
"Helps a ton," Cruz said on Wednesday.
Cruz, 30, has 25 receptions for 377 yards and one touchdown this season. He played more than 90 percent of the snaps through the first seven games. But his playing time already was reduced coming out of the bye week. Dwayne Harris started against the Eagles, and Lewis was on the field for the second drive in Cruz’s regular place.