Bryant acknowledged the setback in a tweet on Friday afternoon, writing: "This is the ultimate test".
Bryant was already having trouble finding a job before the injury - considering it took almost two months of the season before a team took a shot on him.
Bryant, who joined the Saints earlier this week, reportedly suffered the injury on the final play of practice.
If Bryant's injury is officially diagnosed as a torn Achilles, that means we definitely won't see him on the field until the 2019 season.
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The person spoke to The Associated Press Friday on condition of anonymity because the team has not announced any details of Bryant's medical exam. He could have made up to $500,000 in incentives for reaching specific reception totals: $50,000 for catching 25 passes in the Saints' remaining seven games after Sunday, an additional $100,000 for 30 catches, $150,000 for 35 catches and $200,000 for 40 receptions.
The Saints signing Bryant meant he was likely to play against his former team on November 29.
Bryant, in his eight years in Dallas, caught 531 balls for 7,459 yards and 73 touchdowns. The injury came just days after Bryant signed a one-year contract with New Orleans worth up to $1.1 million.