Both sides are interested in a potential deal, according to the newspaper, after the four-year veteran visited the team Saturday and Sunday.
Simpson, 26, could face suspension by the NFL after receiving a 15-day jail sentence and three years of probation earlier this month in connection to a felony drug charge. The Vikings are still gathering information about a possible suspension, the St. Paul Pioneer Press reported.
The Vikings are one of a handful of teams considering Simpson, who opened eyes in December by flipping over a defender and landing on his feet in the end zone. The St. Louis Rams also have shown interest in Simpson, Pro Football Weekly reported.
A second-round draft pick out of Coastal Carolina, Simpson has caught 71 passes for 1,004 yards and seven touchdowns in four seasons with the Cincinnati Bengals.