Clough junior has served a lengthy managerial apprenticeship with Burton Albion, who currently lead the Conference by 10 points.
"It is not because he is a friend or because he is Cloughie's son," said Birtles.
"It is because he is the right man for the job. He could be the son of a bin-man for all I care. This is not about who his dad was, it is about who he is and the fact he has the right attributes for the job.
"It is about the fact he has taken one of the last few remaining part-time Conference sides to the top of the table."