The suitors believe both Leonard and Butler would have interest in playing alongside each other, Begley added.
Both free agents are expected to command max deals on the market this offseason.
Leonard is reportedly seriously considering re-signing with the NBA champion Toronto Raptors, but has been widely linked to other clubs.
The New York Knicks are apparently expecting to meet with the two-time Finals MVP when free agency begins on June 30, while the Los Angeles Clippers are reportedly set to meet with Leonard on July 2. The Los Angeles Lakers can't be ruled out either, as LeBron James has reportedly "had contact" with both players.
Butler was recently connected to the Houston Rockets, but the club doesn't have the cap space needed to land both him and Leonard. The Philadelphia 76ers are said to be aggressive in their attempt to retain Butler.
Leonard averaged career highs in points (26.6) and rebounds (7.3) during the 2018-19 regular season. Meanwhile, Butler averaged 18.2 points on 46.1 percent shooting following his in-season acquisition from the Minnesota Timberwolves.