LeBron James tried to convince Taj Gibson to sign with the Miami Heat.

James and Gibson spent together last summer as the U.S. Select Team prepared Team USA for the London Olympics.

“We talked about it a lot because I was coming up on my contract, possibly becoming a free agent,” Gibson said. ‘‘We were kicking it around, and [James] was saying: ‘Come to Miami. Come in, and we’ll treat you right there.’ I was like, ‘Nah, I’m cool with the Bulls.’ ’’

Gibson signed a four-year extension with the Bulls before the start of this season.

‘‘Very flattering,’’ Gibson said of James’ offer. ‘‘I mean, that shows that there is a sense of respect about your game. It means that there are other guys around the league watching you, other than just going up and down the court and banging bodies against each other.’’