Bosh is the Rockets' plan B as their pursuit of Carmelo Anthony looks to be in doubt.
Bosh's preference is to sign a new deal with the Heat, but with LeBron James still deliberating over where he will play next season the nine-time NBA All-Star has begun considering his options away from Miami.
Houston is Bosh's number one destination if James decides to sign elsewhere, and by putting the max-level deal on the table the Rockets have given the 30-year-old something to think about.
Miami is likely to offer Bosh a deal worth $80-90 million, spread over five years. If he does return to South Beach he is expected to take a pay cut in order to free up cap room to sign other supporting players.
ESPN's Chris Broussard reports that Bosh is "seriously considering" Houston's offer.
Sources: Rockets offer Bosh max deal of 4 yrs, $96 million. After weekend convo with LeBron and low offer from Heat, Bosh considering offer— Chris Broussard (@Chris_Broussard) July 7, 2014
The Rockets' aggressive move for Bosh suggests that they are not confident in their pursuit of James and New York Knicks forward Carmelo Anthony. The team reportedly offered Anthony a similar offer as they did Bosh, but the race for his signature appears to be between the Knicks, Chicago Bulls and Los Angeles Lakers.
Alongside Dwight Howard and Chandler Parsons, Bosh would form a formidable frontcourt in Houston. He is perhaps a better fit for the Rockets than Anthony due to his defensive ability and shooting from the power forward position.