Beckham played his last match for current club Paris St Germain on Saturday night, receiving a standing ovation by the Parc des Princes fans when he was substituted near the end of the 3-1 win over Brest.
A tearful Beckham, who announced this week he was retiring at the end of the current season with the Ligue 1 champions, was made captain for the game and now looks set to miss next weekend's final game away to Lorient.
Keegan and Beckham's former team-mate Ole Gunnar Solskjaer both think he will steer clear of managing and coaching, but have tipped him to still be involved in the game in another capacity.
Keegan told BBC 5 Live's Sportsweek programme: "I don't really see that is where he's going to go."
Keegan sees Beckham taking up some sort of ambassadorial role, whether it be with the Football Association or with a club.
"If you are talking about being around there, a little like Bobby Charlton has done at Man United I suppose, yes, definitely there's a role there (he could do)."
Solskjaer, who won the Champions League with Beckham in 1999 as United enjoyed treble success, does not think management will suit his former team-mate.
"I'm not sure if Becks is cut out to do the coaching. I can see him more on the other side of it," said Solskjaer.
Following the win over Brest, when the 38-year-old made a perhaps telling emotional exit in the 82nd minute by hugging most of his team-mates to a standing ovation before making way for Ezequiel Lavezzi, Beckham revealed he was not keen on playing on Lorient's artificial pitch.
"Tonight [Saturday] was a nice way to go out - in front of my own fans, in front of a capacity crowd that were excited because we've won the league. The celebrations have been incredible, so it's a nice way to walk off the pitch," he said on Sky Sports News.
"To go out like I did tonight [Saturday] couldn't have been any more perfect."
Asked whether he could feature next weekend, he replied: "We'll see. There's a plastic pitch next weekend. I ruptured my Achilles a few years ago, so it's not great for it. Like I said, tonight [Saturday] was very special. I'll be part of the team next week. Whether I play or not, who knows?"
Beckham was particularly touched by the honour of skippering the team and said he would be forever grateful.
"That started my emotions kicking in earlier today [Saturday], when the manager called me in and said 'we've spoken to the players, it's the players' idea - we want to make you captain'," the former England captain said.
"It's really special for an Englishman to be captain of PSG - especially on a night that meant so much to the club and the players. It was an amazing gesture and one I'll always be thankful for."
On his tearful farewell to the players before leaving the field, he continued: "It (the emotion) started 20 minutes before then. The emotions started kicking in.
"It was hard to run, let alone kick a ball. It was an emotional night. To see the reaction of the players, of the fans, when I came off was special."
He added: "Physically, I feel great. I actually felt great tonight [Saturday]. Physically, I think I've made the decision knowing that I wanted to still feel good at the end of my career and I do feel good. But I know it's the right time."
Beckham, who joined PSG in the winter on a short-term deal, has won league titles in four countries - England, Spain, the United States and France.