The Warriors have reportedly barely spoken with Thompson over the past two weeks.
The 34-year-old averaged 22.6 points (on 47/41/91 shooting splits), 5.2 rebounds and 3.5 assists per game this past season, leading the Clippers to the first round of the playoffs.
James is eligible to sign a three-year, $162 million maximum contract to return to the Lakers in free agency.
Love, a five-time All-Star, signed with the Heat in 2023 and is reportedly hoping to negotiate a new deal during free agency.