The Vikings acquired Vedvik in a trade with the Baltimore Ravens Sunday, sending a fifth round pick in the 2020 NFL Draft in the exchange for the former Marshall special teams star.
"I might have him play safety, maybe he can play outside linebacker, I don't know," Zimmer told reporters Monday.
Vedvik had two punts for an average of 55.5 yards in the Ravens' preseason game against the Jacksonville Jaguars Aug. 8 in Baltimore. He also made field goals from 55 yards, 45 yards, 26 yards and 29 yards.
The Norway native made 10-of-16 field goal attempts and 41-of-42 extra point attempts during his senior season at Marshall. He also averaged 44 yards per punt in his final season with the Thundering Herd.
"Yeah, if he's good enough, I don't have a problem with that," Zimmer said of Vedvik's potential to punt and kick for the Vikings. "But I don't know. Again, I think everything is a possibility at this point."
Vedvik will compete with Dan Bailey for the kicking job and Matt Wile for a punting gig. If he replaced both players, it could allow the Vikings to have more flexibility on their roster.
"It's probably difficult for a rookie [to punt and kick] I would think," Zimmer said. "You'd have a rookie snapper and a rookie punter and rookie kicker. Then you would have to find somebody to hold."
Bailey, 31, made just 75 percent of his kicks last season, converting on 21-of-28 attempts. He made 96.8 percent of his extra points. The eight-year veteran is the fifth-most accurate kicker in NFL history, making 86.6 percent of his career field goal attempts. Bailey made the Pro Bowl in 2015, leading the league by making 93.8 percent of his field goals while with the Dallas Cowboys.
Wile, 27, averaged 45.2 yards per punt last season for the Vikings. Bailey and Wile are both playing on one-year contracts with the Vikings in 2019.
Zimmer said he still likes Dan Bailey "a lot."
The Vikings host the Seattle Seahawks in a preseason game at 8 p.m. EDT Sunday at U.S. Bank Stadium in Minneapolis.