But a conversation with James about his future in Miami this past weekend created enough doubt for Bosh to begin considering his other options, including Houston's offer, a source said. The source said Bosh did not know whether James was staying in Miami.
Another factor in Bosh's decision to look at Houston has been the tenor of his negotiations with Miami. Bosh is willing to take an annual pay cut by accepting a five-year deal worth $80-90 million from Miami. But sources say the Heat have been trying to get Bosh to accept a lesser deal, obviously so they can have more money to spend in free agency.
The Heat's "low-balling" -- plus his conversation with James -- has led Bosh to take a serious look at Houston's offer, which could approach $90 million as it can change slightly.
The Rockets made the same max offer to Carmelo Anthony, but they have come to believe he will not accept it.
Houston will have to trade Jeremy Lin to create the cap space to offer the max to Bosh, but the Rockets are confident they will be able to do that in short order.