"We have received an unconfirmed report that John McAfee has been captured at the border of Belize and Mexico," his official blog whoismcafee.com said on Saturday.
The website, which McAfee launched to counter what he sees as erroneous claims by the media or authorities about him, said that it would provide more information as it became available.
Police say they simply want to question the 67-year-old about the murder of fellow American Gregory Faull, a Florida native who was found dead last month in a pool of blood at his home on the Caribbean island of Ambergris Caye.
Faull, 52, was shot in the back of the head, according to a police report. There were no signs of a break-in, and a laptop and mobile phone were missing.
McAfee has said that he fears for his life and was fleeing authorities with whom he has been at odds with ever since refusing to make a donation to a local politician's campaign.