The Daily Mail says Martinez spoke to Villa on his return from a break in Barbados and is now in pole position to succeed Gerard Houllier, who left last week because of health problems.
Martinez, who was given permission by Wigan chairman Dave Whelan to talk to Villa, ticks all the boxes as far as owner Randy Lerner is concerned - especially when it comes to working on a tight budget.
"I'd be surprised if he is Villa's new manager," said Whelan. "I have made it clear to him that I will be extending his contract.
"Villa have acted above board and in a totally professional manner throughout. They wrote to me asking for permission to speak to Roberto. He was on holiday at the time and I granted Villa permission."