Brooking said he had never pushed Curbishley for the job.
"I have not expressed a preference for any potential candidate, either publicly or privately," Brooking said. "Specifically, it is completely untrue that I have been backing Alan Curbishley for the job. I have never been asked about Alan."
"Brian and I are extremely annoyed at what appears to be an effort to destabilize our work together to find the next England manager, but we will continue to move forward together in the same positive manner," he said.
The FA also cooled speculation that it has drawn up a shortlist of coaches. British newspapers have suggested that Mourinho, Curbishley, Aston Villa's Martin O'Neill, former AC Milan and Real Madrid coach Fabio Capello, former Germany coach Juergen Klinsmann and Italy World Cup winner Marcello Lippi are the FA's leading candidates.
The bookmakers have made Mourinho the favorite at 6-4, with Capello next at 2-1. Curbishley is at 50-1.
Mourinho came to Chelsea in June 2004 after guiding FC Porto to the Champions League title. He led Chelsea to their first league championship in 50 years followed by another the following season and also took the Blues to League Cup and FA Cup triumphs.
Capello, by contrast, has no experience of English soccer. He spent his entire career as a player or coach either in Italy or Spain.
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