Spaniard Jon Rahm, Fleetwood’s Ryder Cup teammate, became the latest big name to join LIV in December.
Several high-profile players have been lured from the PGA Tour to join LIV, thanks to its larger prize pools and no-cut events.
Negotiations between the PIF, which finances LIV Golf, and the PGA Tour on the alignment did not result in an agreement at the end of 2023.
Talks have continued this year, but Fleetwood says he has no plans to change companies.
“There’s nothing really. There’s nothing happening,” Fleetwood told BBC Sport at the Dubai Desert Classic.
“I played here [in Dubai] for two years and I still play here now. I’m pretty boring when it comes to news and that’s exactly what it is.
“People have been approached for a long, long time now, so I don’t think it’s breaking news that people are still being approached by LIV. Some people will go and some people won’t. At some point we all will play together, otherwise we won’t. Like everyone else, I’ll just wait to find out.
“I’m still chasing my childhood dreams and still trying to be the best golfer I can be. Who knows if that will change in the future, but for now, that’s exactly where I want to be.”
Fleetwood’s compatriot Tyrrell Hatton, world number 15, partnered Rahm in the Ryder Cup last September.
“Several people have had conversations. I think it’s a natural part of golf right now,” Hatton said. “But I’m pretty happy playing on the PGA Tour and the DP World Tour.”
When asked if he was happy to remain on the PGA Tour and DP Tour, Hatton replied: “For now, yes.”