Schefter noted Reed is currently healthy despite his history of concussions.
The 30-year-old missed the entire 2019 season after suffering the seventh recorded concussion of his career, but he was cleared by the league's concussion protocol program in February, per Ben Standig of The Athletic.
Reed has spent his entire NFL career with the Washington Football Team but has only appeared in 65 of 112 possible regular-season games since entering the league in 2013.
He was a star at his position when healthy, finishing the 2015 season with 87 catches for 952 yards and 11 touchdowns. The next season he earned his lone Pro Bowl selection with 66 catches for 686 yards in just 12 games.
Though he hasn't been the same since, the 49ers are taking on a gamble that he can recreate the production he had earlier in his career.
Reed also reconnects with San Francisco head coach Kyle Shanahan, who was his first offensive coordinator with Washington in 2013.
The 49ers already have one of the top tight ends in the NFL in George Kittle, but Reed could provide some help in two-tight end sets while competing with Ross Dwelley and Charlie Woerner for playing time.
With Kittle also set to enter free agency next offseason, the signing could provide some assurance in case the 49ers can't agree to an extension with their Pro Bowler.