Wolf is the second Badgers quarterback to reportedly test positive for COVID-19.
Wisconsin might be turning to its fourth-string quarterback this week after Chase Wolf also tested positive for COVID-19, according to the Milwaukee Journal Sentinel.
The Journal Sentinel reports Wolf, the Badgers' third-string QB, missed Monday's practice. News of his test comes after the Milwaukee Journal-Sentinel and Wisconsin State Journal reported that starter Graham Mertz tested positive over the weekend.
Both papers reported that Mertz would be undergoing a polymerase chain reaction (PCR) test to determine if the first result was a false positive. Wolf will also take a PCR test to confirm his first result. If confirmed, the players will sit out at least 21 days, per Big Ten protocol, and Wisconsin will turn to redshirt junior Danny Vanden Boom to face Nebraska on Saturday.
The Badgers are already missing starting quarterback Jack Coan, who is out indefinitely after undergoing foot surgery on Oct. 6.
On Sunday night, Wisconsin issued a statement saying it will not release "COVID-related testing information regarding any individual student-athlete, due to medical privacy."
Coach Paul Chryst wouldn't discuss Mertz's status with the media on Monday following the reports of his positive test.
"I will not, cannot and should not, therefore, comment about anything dealing with our testing and coronavirus," Chryst said.
Chryst did say he was confident the ninth-ranked Badgers' game Saturday at Nebraska (0-1) would go on as scheduled. He added that he has no problem with the Big Ten's 21-day policy, which is more stringent than those of most conferences regarding players who test positive.
Mertz shined for the Badgers in their opening-night win over Illinois on Friday. The redshirt freshman completed 20 of 21 passes in the 45-7 victory, throwing for 248 yards and five touchdowns.
Vanden Boom appeared in three games in 2018 and completed his only pass attempt for a touchdown.
Wisconsin (1-0) visits Nebraska, hosts Purdue and travels to No. 13 Michigan in its next three games.
The Associated Press contributed to this report.