Spanish businessman Enrique Riquelme is also in the running.
The Northern Irishman stopped off at Shinnecock Hills on Long Island in New York on Monday on his way to this week’s Memorial Tournament in Ohio.
Lawes retired from Test rugby after the 2023 World Cup but his ambitions of returning to the global stage have been rekindled.
Stokes fears a hard-line stance could see the likes of Archer desert international cricket.