Ballmer outbid two groups, one led by media mogul David Geffen that offered $1.6 billion and another from Los Angeles investors who bid $1.2 billion.
An official representing Ballmer had no immediate comment.
The Clippers came up for sale after the NBA banned owner Donald Sterling for life because of racist remarks he made in a recorded conversation that was leaked last month to TMZ.com.Sterling, who has vowed to fight the NBA's punishment, would have to approve the sale, as would league owners.