The Brazilian turned his loan spell from Barcelona into a permanent deal last week for £17million.
Gerrard has previously ranked Suarez above Fernando Torres as the best forward he played with during his time at Liverpool.
Suarez spent three years at Anfield between 2011 and 2014, notching up 82 goals from 133 appearances.
The Uruguayan star is set to become a free agent this summer. Suarez has spent two seasons with Atletico Madrid and finished top goalscorer in 2020/21 with 20 goals as Diego Simeone's side won La Liga.
Despite only 11 goals this term, Petrov labelled 35-year-old Suarez "world class" and said he can still deliver goals with the right players around him.
"I'm not surprised at all. Suarez is a world class striker. A lot of people were surprised - can he still do it? As long as you have the right quality players around them," Petrov told Planet Sport.
"A lot of people question the years and everything else but you don't have to forget that if you balance your team well you can use their strength in a different way.
"But I'm not surprised. This is the profile Steven Gerrard is - everybody knows the way he manages and his desire to win," Petrov continued.
"So players that have played with Steven Gerrard and the players that know Steven Gerrard or players that are going to firstly speak with Steven Gerrard will find out his profile and what he's like as a manager and as a person mainly.
"I'm not surprised that a high profile players have been linked with Villa again."
Petrov - who captained Villa and experienced three seasons in Europe under Martin O'Neill - said they need to "strengthen in every area" if they are to qualify for European positions next season.
"He's [Gerrard] just showing that signing Coutinho early before the start of next season (he can attract quality players). He's going to be available for a full pre-season and that's what Coutinho needs - a full pre-season, going back to his routines and back to full match fitness.
"Signing Coutinho is showing that the ambitions are high so they do need to strengthen in every area because fighting for Europe - you know the Premier League will be much stronger next year. He'll be embracing that challenge."