The clubs will contest a Premiership tie at Free State Stadium, with Middendorp swapping Maritzburg United for Phunya Sele Sele last week.
"Obviously there will be unique challenges myself as the new coach and the players will face," Middendorp told Celtic's official website.
"When a new coach comes in during a season it is always difficult to imprint his style straight away but I want to win this match as I do all matches and I have been preparing the best I can for this game against a very good Swallows team.
"I am looking forward to playing at home, in front of the fantastic Celtic crowd and I hope they turn up in numbers to become a 12th man, like they have on so many occasions.
"I am still learning the players strengths and weaknesses but I believe Celtic is a really quality side, with many experienced and talented players and if I didn’t think this team would go places, I would not have decided to come here," concluded the German.