Fox Sports' Jay Glazer reported on Twitter that Moss ran about 45 routes in the workout and impressed the Saints with the way he performed. An NFL source told ProFootballTalk.com that Moss' workout "couldn't have gone better."
Saints general manager Mickey Loomis said the club held a workout with Moss but the team is not releasing details of the session.
Colston's agent is Joel Segal, who also represents Moss.
"Randy had an outstanding workout, as expected," Segal said. "He's in phenomenal shape."
Moss announced on his 35th birthday that he was ending his one-year retirement from the NFL.
The 6-foot-4 Moss last played in the NFL in 2010, a turbulent season for him in which he bounced from New England to Minnesota and then to Tennessee.
Moss' 153 touchdown receptions are tied with Terrell Owens for second on the career list. He's fifth all-time in yards and ninth in receptions. His 29 touchdowns of at least 50 yards are behind only Jerry Rice (36).
He led the NFL in touchdown receptions five times, was selected to the Pro Bowl six times and was named first-team All-Pro four times. His 23 TDs in 2007 led the entire NFL and his 138 points scored that season were second only to kicker Mason Crosby.
Moss has had more than 1,000 yards receiving in a season 10 times, second only to Rice, who did that 14 times.
Yet he also infamously once said, "I play when I want to play," essentially confirming criticism that he periodically took plays off when the ball wasn't coming to him.
During the 2010 season, after he had been traded from New England to Minnesota, then played for the Vikings in a loss to the Patriots, he praised New England coach Bill Belichick and criticized Vikings coaches. He was released by Minnesota shortly afterward and claimed by Tennessee for the final eight games of the season, but had only six receptions for 80 yards and no TDs for the Titans.
Saints coach Sean Payton has often spoken of placing a priority on players' character and limiting off-the-field distractions, but the coach is apparently open to seeing whether Moss can still play, and giving the receiver a chance to persuade him that some of the odd outbursts for which he has been known are a thing of the past.
Information from The Associated Press was used in this report.