Adelaide will join the race for Beckham, but Fyfe reckons the Reds are a long-shot.
"I see him sitting courtside at LA Lakers games, I don't think he's going to come here and sit courtside at Adelaide 36ers games," Fyfe told reporters on Tuesday.
"I think he's more used to a glamorous lifestyle personally."
Fyfe believed Football Federation Australia (FFA) would prefer Beckham at a club in a state with a larger stadium than Adelaide's 15,000 capacity Hindmarsh Stadium.
"It's probably the bigger city clubs that will pursue him a little bit harder, just in terms of crowd numbers," Fyfe said.
"When you think a guy like that, I played against him for Sydney against LA Galaxy, he drew 80,000 people to the game.
"We can only hold 15,000 so in terms of the FFA and how they want to set it up, it would be great to have him here, but realistically I think the FFA would prefer him to go to a state with a big stadium."