Denver, Boston and Philadelphia are mentioned in the report.
The Nuggets have interest in acquiring Love, while the Sixers could include forward Thaddeus Young to abet another team's pursuit of Love.
Boston is also targeting Love but would offer draft picks in exchange for a different player capable of contributing 'immediately.'
“When a deal like this takes a long time, there are going to be more ants circling the picnic," one front-office source told Sporting News. "This is not likely to be a one-to-one trade."
Cleveland's package would include Andrew Wiggins and Anthony Bennett, the No. 1 picks in the last two drafts, plus a future first-rounder and potentially one additional player to meet NBA trade requirements.
Other potential landing spots for Love include Golden State and Chicago.
Love, 25, is said to be intent on leaving Minnesota if the team does not trade him before the end of next season, when he can opt out of the final year of his contract to become an unrestricted free agent.
He averaged 26.1 points and 12.5 rebounds a game last season as the Timberwolves won 40 games and missed the playoffs.
- Chris Johnson