Keane is currently working under Republic of Ireland boss Martin O'Neill, but is said to be in talks with Villa over a possible switch to the Midlands outfit.
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The former Manchester United captain had been in talks to take the vacant manager's role at Celtic, before breaking off discussions last week.
After former number two Ian Culverhouse was dismissed for unspecified off-field matters, a vacancy has opened up at Villa Park and Vlaar believes Keane would be perfect for the role.
"I don't know him as a person, I know him as a player," he told The Birmingham Mail.
"He has a lot of fighting spirit, and I think that would be really good for us.
"He's a very strong character. I think everybody has a lot of respect for him and I look forward to it."