The England skipper's vacancy is available after Gerrard's retirement from the international scene following the World Cup.
"I think Wayne has grown and he is growing into that role," Ferdinand, who captained England for 13 months from February 2010, was quoted as saying in various British media on Wednesday.
Ferdinand added: "He's experienced now, he has played at the top level and he's won a lot of things.
"He knows the game. He's got the right tools for that. And I think you have to look at who is going to start."
Rooney has scored 40 international goals since making his debut as England's youngest ever player against Australia in February 2003.
The 28-year-old's underwhelming performances in his country's first round knockout in Brazil came under heavy scrutiny but he answered some of his critics with a second-half goal in the defeat to Uruguay.
"You look at other countries, the natural progression would be Wayne getting it now," Ferdinand continued.
"With other countries it's usually the guy with the most caps, or who is most influential.
"And I think Wayne is the most influential player that England have got at the moment, now Steven has gone.
"It would seem like a natural progression."
With Gerrard gone, the pressure on Rooney to deliver will only increase but Ferdinand believes wearing the armband should not be a burden.
"With the captaincy, especially in England, we maybe go a bit overboard on it," Ferdinand added.
"You need as many leaders out on the pitch as you can get.
"You need people to lead by example, not just on the pitch but off the pitch. Hopefully we have got a few in there that can do that."
- Sports & Recreation
- Rio Ferdinand
- Wayne Rooney
- Steven Gerrard