The Scot was placed in caretaker charge of the club in late March following Remi Garde's departure.
Black, 52, originally joined Villa from Rotherham United in late January to work as a first-team coach under Remi Garde but was placed in caretaker charge for the remainder of the season following the Frenchman’s departure at the end of March.
The Scot has since failed to record a win in his six games at the helm, however, while the club’s inevitable relegation was confirmed with four matches to spare following last month’s 1-0 loss at Manchester United.
Nevertheless, his side have shown some signs of progress over their last two fixtures, having come within minutes of winning at Watford before losing 3-2 to two late goals and then held Newcastle United to a 0-0 draw last weekend to halt a club-record equalling 11-game losing run.
Sunday afternoon’s match will now mark the end of his temporary tenure, and while the ex-Coventry City boss would like to remain on the backroom staff, he admits that he expects to be forced to move on this summer when a new manager in appointed.
Speaking at his pre-match press conference, Black said: "I've been told to take the team until the last game. I'd imagine that will be it for me on Sunday but I'll just wait and see. That will all be out of my hands, like one or two others. I'm sure there are other staff in a similar position to myself .
"But it is what it is, it's football. Obviously Aston Villa at the moment is slightly more complex as there's potential new owners coming in and there's obviously a new manager coming in so we'll have to wait and see.
"I'm aware of that, I've been in football a long time so I'll just continue to do what I'm asked to do and see where it goes.
"There's nothing at all in place for after Sunday,” he continued. “I spoke to the chairman very briefly this [Friday] morning and he just thanked me again for keeping things going at the moment. But as I said, come five o'clock on Sunday it's just a case of waiting to see what happens.
"Whatever happens I can hold my head high, definitely. I'm quite comfortable with that. A lot of people will have their own opinion on that, many of which will probably be that I should have won more games or been slightly more adventurous, but I can live with all that.
"I had to do things in a certain way under difficult circumstances so I will walk away and we'll see what happens."
A handful of Villa players are set to miss the Arsenal game through injury, meanwhile, with Ciaran Clark [ankle], Alan Hutton [calf], Kieran Richardson [calf] and Jordan Veretout [hip] all doubtful to feature as the club bid farewell to the top-flight at the Emirates Stadium.
Rudy Gestede could return to the line-up, however, after recovering from a groin problem, while Aly Cissokho is available for selection again following a one-match suspension for his sending off against Watford.
Youngsters Jordan Lyden, Kevin Toner and Rushian-Hepburn Murphy are also expected to be involved on the afternoon, while Jack Grealish is pushing for his first top-flight start in over four months.