England is on the hunt for a new manager after Roy Hodgson vacated his role after the nation's embarrassing last-16 exit to Iceland at UEFA EURO 2016 last month.
Sunderland's Sam Allardyce has emerged as the frontrunner, having reportedly met with FA officials, while Bruce has put his hand up for the job after guiding Hull City back into the Premier League.
"No, nothing yet," Bruce told the Daily Mail when asked if he had received a call from the FA.
"Of course, I'd love the call. It would be a highlight to help England.
"I've been at this the thick end of 40 years. Nearly a thousand games as a player, nearly 800 as a manager. That's a lot of Saturday afternoons."
United States boss Jurgen Klinsmann has also been linked with the vacancy, the German believed to be in a two-way race with Allardyce to replace Hodgson.
Arsene Wenger and Laurent Blanc are two other names reportedly in consideration.
However, Bruce insists: 'The England manager should be English. Even if it's not me, it should be an Englishman."