Villa owner Randy Lerner remains a big fan of Martinez even though the Spaniard rejected the chance to take charge of the midlands club 12 months ago.
Lerner is searching for a hungry and emerging figure to revive Villa's fortunes and maintains that Martinez fits the bill.
Martinez's desire to play an attractive style of football has also impressed Lerner after fans were critical of the approach of the sacked Alex McLeish.
Lerner is aware of the interest of Liverpool in Martinez and knows he runs the risk of being delivered a knockback by the 38-year-old for a second successive summer.
But it is understood Lerner has received sufficient encouragement to believe Martinez would at least discuss his proposals and hopes he can offer an attractive package and picture of Villa's future.
Paul Lambert (Norwich), Brendan Rodgers (Swansea) and Gus Poyet (Brighton) are other potential candidates on Villa's radar as they search for a fourth manager in two years.
Lerner flew back to England two days ago from America to step up the managerial search.
Ole Gunnar Solskjaer had been the bookmakers' favourite to replace McLeish but he has opted to stay in Norway with Molde for family reasons.
Villa insist the former Manchester United striker was never offered the job after he was interviewed last weekend by Lerner.