The Sydney Sixers franchise are hoping to lure him for the December tournament, after Bolt made clear he wanted to turn out for the Melbourne Stars.
Like Bolt, Blake is from Jamaica and cricket-mad, and Sixers chief executive Stuart Clark said he was keen on setting up a clash between the close friends.
"For one he is a great athlete, and yes he would be a marketer's dream, but from all reports he can actually play cricket and that's better than anything else," Clark told the Sydney Daily Telegraph.
"If he can do what he says he can do, and I have no reason to disbelieve him, Yohan would be a marquee player for me to sign. I would definitely be considering it."
Earlier this week, Shane Warne revealed he was leading a campaign to bring Bolt to Melbourne, with negotiations under way with the Melbourne Stars, the Australian former Test leg-spinner's club.
Bolt played junior cricket before turning to the track and has long voiced a love for the game.
"He (Warne) contacted me and asked me about if I am serious and if I really want to do it, then he can put in a few words that should get it done," Bolt told Australian television.
"So we will see if I get the time off. I will try."
Cricket is hugely popular in the West Indies with Jamaica one of its strongest teams, producing greats such as Michael Holding, Courtney Walsh and Chris Gayle.
According to the Telegraph, Blake, who took silver in the Olympic 100m and 200m events behind Bolt, says he is "a bowling machine".
"You guys need to see me in action. I am a bowling machine that can bat all day," he reportedly said during the Olympics. "Cricket, that's my love, that's my passion."
Clark said: "I will need to see some footage of him bowling, but he has been saying he can bowl 90 miles per hour (145 kilometres per hour). Very few people in the world can do that.
"Usain Bolt is a great showman and entertainer, but he can't play cricket as far as I'm aware, to the standard necessary. Yohan Blake can, it seems."
The newspaper said Australian agent Tony Connelly was brokering the deal between Blake and the eight-team Big Bash, which was launched last year to attract a new youthful audience to cricket.
The season, where each side tries to blast as many runs as possible in a maximum of 20 overs, gets under way on December 7 with the final on January 19.
While national selector John Inverarity admitted Bolt and Blake would be massive drawcards, he cautioned about the Big Bash becoming "a novelty event".
"T20 cricket is very much entertainment, it's a very heavy focus on just being entertainment, so he (Bolt) would certainly be a drawcard," Inverarity told reporters after announcing Australia's World Twenty20 squad.
"I'd be hesitant to run two if you hit one just wide to him on the boundary. I can imagine he'd throw very well too.
"But I think we've got to be careful it just doesn't become a novelty event."