Villa, who have three wins in 11 games and are 13th in the table, sacked Steve Bruce on Wednesday and named under-23 boss Kevin Macdonald as caretaker. The club said they have begun the search for Bruce's successor.
"I've made the necessary move and I've sent in my CV and I'm actually trying to make contact with the chief executive of the football club," former Sydney FC star Yorke told Sky Sports.
"I played for them and understand the club and understand what the fans expect. I feel I can bring a winning mentality back to the football club."
Yorke, who scored 97 goals in more than 250 appearances for Villa before joining Manchester United, had expressed a similar desire to take over when Tim Sherwood was sacked in 2015.
"He (Sherwood) gave me an insight into what he might have failed on, so having that knowledge does give me more of an insight in what is needed at the football club," Yorke added.
Yorke's previous coaching experience includes a stint as assistant manager of his native Trinidad and Tobago between 2009 and 2010.
Former European champions Villa were held to a 3-3 draw at home by Preston North End in midweek, a result that was followed by Bruce's sacking. They travel to Millwall this weekend.
Former Manchester United and Everton manager Davis Moyes is the bookmakers' favourite for the job followed by former France and Arsenal striker Thierry Henry, who was linked with the post in the close season, and experienced Portuguese Paulo Sousa, who left Chinese Super League club Tianjin Quanjian on Thursday.
