Perry made the comment after a taping Wednesday of the television program "Inside Texas Politics" at the WFAA-TV studios in Dallas. He said Abbott "has said clearly that if I ran again he's not going to be running against me."
A spokesman for Abbott declined to comment on Perry's statement and said any speculation on Abbott's political future would be "unproductive."
Abbott has $18 million in cash on hand for a campaign, compared to Perry's $6 million. Perry hasn't said if he'll seek re-election as governor, but observers have said they expect Abbott may enter the Republican gubernatorial primary regardless of what Perry does.