The band of Republican politicians, according to the Post, is attempting to block presumptive GOP presidential nominee Donald Trump and believes that Cuban, the outspoken billionaire owner of the Dallas Mavericks, would resonate with voters.
Although he said he would "put [Trump] in his place," Cuban told the Post that he does not anticipate running for president this year, saying "there isn't enough time."
"I don't see it happening," Cuban wrote in an email to the newspaper.
Asked by ESPN.com on Sunday if he would consider running for president four years from now, Cuban replied, "No comment."
Cuban declined to identify the anti-Trump Republicans to the Post, although he did reveal that the conservative group told him that he could challenge Trump because of his "bluster and volume, combined with substance and the ability to connect with voters on a more personal basis."
"[Trump] could come after me all he wanted, and he knows I would put him in his place," Cuban said. "All that said, again, I don't see it happening. There isn't enough time."
Cuban, 57, became the Mavericks' majority owner in 2000 and helped revive the franchise into a perennial playoff team. The Mavericks won their only NBA championship in 2011 and have missed the playoffs only twice in 17 seasons since Cuban bought the team.
Information from ESPN's Tim MacMahon was used in this report.