Brian Horton parted company with the Silkmen after their relegation from League Two was confirmed last month, with the club stating their desire to appoint a manager with specific knowledge of the Blue Square Bet Premier.
Former Manchester City boss Horton replaced Gary Simpson in March but was unable to turn around a dismal series of results that ended with Macc finishing bottom of the fourth tier and without a victory.
"We're very encouraged by the level of interest in the opportunity," Rance told Macclesfield's official website.
"We've received more than 40 serious applications, many of them with impressive CVs.
"While getting appointment right is paramount, we would also like to complete the process as soon as possible."