Bryant, who turns 30 in November, wants a one-year deal and a chance to prove himself, in hopes of getting a bigger long-term deal in 2019, sources said.
The news was first reported by The Doomsday Podcast's Ed Werder.
The Ravens' interest in Bryant dates back to the 2010 draft, when it appeared they were going to have a shot at selecting him with the No. 25 overall pick. But the Cowboys traded three spots up and chose Bryant just ahead of Baltimore.
After Bryant turned down the offer, the Ravens signed receiver Willie Snead.
The Cowboys released Bryant on April 13. He played eight seasons in Dallas and finished his time with the Cowboys with a team-record 73 touchdown receptions to go with 531 catches for 7,459 yards in 113 games.
Bryant amassed more than 1,000 yards receiving, with double-digit touchdowns, for three straight seasons from 2012 to 2014. But his production slipped after signing a five-year, $70 million contract in 2015. He did not record a 1,000-yard season over the next three years and was slowed by foot and knee injuries. He played in every game last season and had 69 catches for 838 yards and six touchdowns.
Bryant was set to make $12.5 million this season. He has said about his exit from Dallas that he "should've been better at controlling my emotions" and that he "should've been a better professional," but added that football is "the love of my life."
ESPN's Jamison Hensley contributed to this report.