Given's £3.5million move from City is expected to go through later this week subject to a successful medical.
It will be new Villa manager Alex McLeish's first signing since replacing Gerard Houllier last month.
Petrov was sorry to see Friedel leave Villa - for Tottenham - after a three-year spell but is confident 35-year-old Given will fill the void.
The Bulgaria international said: "Shay is one of the best keepers in the league and, if he comes to us, it will be a great signing for us.
"He's got European experience and Premier League experience so what else do you need?
"Brad Friedel was a big loss. He played a major part at this club and I was sad to see him go.
"He was outstanding for us, for his age, and he showed everybody it doesn't matter how old you are.
"He's signed another two year contract (at Tottenham) at the age of 40.
"But Shay would be a great signing and I hope that could happen."