Tommy Fleetwood and Tyrrell Hatton reject LIV Golf advances
Fleetwood and Hatton both sit in the top 15 of the world rankings and helped Europe to Ryder Cup glory last year.
Reigning Masters champion Jon Rahm joined LIV last month in a deal reportedly worth hundreds of millions of dollars in a huge coup for the upstart tour.
The Spaniard's move has sparked a frenzy over which other star names could turn their backs on golf's traditional tours with LIV Golf chief executive Greg Norman promising "more apples falling from the tree".
However, Fleetwood and Hatton, who are in action this week at the Dubai Desert Classic, said they are happy to remain where they are for now.
"I'll always be doing what I think is best for my golf game and at the moment that is what I am doing," Fleetwood told the BBC.
"People have been getting approached for a long, long time now so I don't think it's flash news that people are still being approached by LIV.
"Some people will go and some people won't. At some point we'll either all play together, or we won't. I, like everybody else, will 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 changes in the future but for now that's just where I want to be."
A proposed merger between the PGA Tour and the Saudi Public Investment Fund, which backs LIV, appears to have stalled after the deadline set to agree a framework for the joint venture passed on December 31st.
Hatton, who successfully teamed up with Rahm at the Ryder Cup last year, had been one of those rumoured to be set to follow the two-time major champion to LIV.
"There's several people that have had conversations. I think that's part and parcel of golf at the moment," said Hatton. "But I'm quite happy playing the PGA Tour and DP World Tour."
Asked if he was happy to remain on both circuits, Hatton added: "As of right now, yeah."