Swansea are close to completing a shortlist in their search for a new manager.
Potter left Swansea last month after less than a year in charge to become manager at Brighton, who had sacked Chris Hughton a week earlier.
"The fact that we have had so many quality applicants speaks volumes on how attractive and well respected this football club is within the game," Birch told the club's official website.
"We still have some more candidates to interview early this week, after which, we will have a much clearer picture on how we are going to progress and move to our final shortlist
"It is important we don't rush the appointment. But it's more important that we make the right appointment. I will endeavour to keep supporters updated as things progress."
Swansea finished the season in 10th place under Potter, who joined them from Swedish side Ostersunds FK in June 2018 after Carlos Carvalhal's departure.