Capello will leave the role at the end of England's Euro 2012 campaign and Wenger had recently been rumoured as a possible replacement.
However, Wenger effectively ruled himself out of contention for the position with his stance on the need for a home-grown boss.
"I always said the national team needs an English manager and I will never change that for one minute," said the Arsenal manager.
"If a foreigner wins a European Championship, you will say somewhere it is not completely an English triumph."
Wenger has come under increasing pressure as Arsenal find themselves languishing in fifteenth place in the Premier League table.
Capello is England's second foreign manager in the last decade after Sven-Goran Eriksson's spell from 2001 to 2006.