Martinez has been linked with the Italian giants throughout the window, and reports had even claimed the Argentina international had reached an agreement with Juventus over a move to Turin. Vidagany, though, has now dismissed the speculation in emphatic fashion.
"The goalkeeper's future is settled, he is staying with us, and we have no intention of letting him go this summer," he told 365Scores.
"The team needs his efforts and extensive experience, and he is a very important element in our project for next season."
The Villa chief made clear he is well aware of the constant stream of stories connecting his number one with Juventus, but insisted they bear no relation to the club's thinking.
"All the news published by the media about his departure to Juventus does not reflect the club's true position.
"Martinez is a very important player for us, and we expect him to continue delivering his outstanding performances alongside his team-mates."
The comments amount to a firm rebuttal of reports in Italy, where Sky Italia had claimed Martinez agreed a three-year contract with Juventus and was even prepared to take a pay cut to push the move through. Villa's public stance suggests any such arrangement, if it exists, will count for little.
The 33-year-old is under contract at Villa Park until the summer of 2029, leaving the club under no pressure whatsoever to cash in, and his importance to the team is difficult to overstate. Martinez has been a cornerstone of Villa's rise in recent seasons and is regarded as one of the finest goalkeepers in the world.
Retaining him carries added significance given what lies ahead. Villa will compete in the Champions League next season, and Vidagany's remarks underline the club's determination to attack the campaign with their strongest possible squad rather than dismantle it.
Martinez, for his part, is currently occupied with rather more immediate concerns. The goalkeeper is on World Cup duty with Argentina, who face England in Wednesday's semi-final as the holders close in on another shot at the trophy.
A central figure in Argentina's triumph four years ago, Martinez will return to club football with his future resolved, and Juventus will be forced to look elsewhere in their search for a new number one. For Villa supporters, the message from the top could hardly have been clearer: their goalkeeper is staying put.