Rapoport tweeted the Saints are "pushing really hard to get him."
Asomugha, 31, is considered one of the top cornerbacks available on the market. He spent the last two seasons with the Philadelphia Eagles before hitting free agency.
David Fucillo of Niners Nation writes it could be a while until Asomugha decides where to land. He says it would be smart for Asomugha to find a new team before the draft, so teams don't fill secondary holes with rookies.
Asomugha was highly touted after spending eight years as an Oakland Raider, but many considered his time with the Eagles as a disappointment. In 32 games with the Eagles he recorded 94 total tackles, four interceptions and 16 pass deflections.
After picking off eight passes in 2006, quarterbacks stopped throwing his way. He's recorded just seven interceptions in six seasons since that breakout year.