"The Bulls and Knicks' competition stretched beyond the Bulls' 118-85 blowout victory Tuesday night, achieved without the services of Joakim Noah.
The teams also are in battle for Tracy McGrady's expiring $22 million contract.
League sources said the Bulls have offered Brad Miller, Tyrus Thomas and either Kirk Hinrich or John Salmons to the Rockets for McGrady, who has been granted a leave and is training in Chicago.
The Rockets have shown little interest in either Hinrich or Salmons and thus, sources said, the Bulls have tried to recruit a third team to get involved. It's also possible the Bulls have made another unknown offer with a player replacing Hinrich or Salmons to the Rockets."