"We're always looking for good players to improve our team and we think Nnamdi would be a great fit for our defense and our team," Loomis said, adding the Saints are waiting for Asomugha to decide where he wants to play.
Asomugha, who turns 32 in July, also visited the 49ers last week.
Asomugha was at his best when he played for Rob Ryan in Oakland. Ryan is the Saints' new defensive coordinator.
The 6-2, 210-pound corner played for Ryan from 2004-08. He was a first-team All-Pro in 2008 and a second-teamer in 2006 when he made eight interceptions, returning four for touchdowns. Asomugha also made first-team All-Pro in 2010 after Ryan's departure, and three straight Pro Bowls from 2008-10.
New Orleans needs all the help it can get after giving up an NFL-record 7,042 yards (440.1 per game) and ranking 31st in both pass defense and points allowed.
If Asomugha signs, the Saints could release Robinson or Greer, according to the Times-Picayune.
For more NFL news, rumors and analysis, follow @EyeOnNFL on Twitter, subscribe to our RSS Feed, watch Pro Football 360 daily at 3 ET and NFL newsletter. You can also follow Larry Hartstein @LarryHartstein.