The Swans have enjoyed an excellent campaign this season, winning the Capital One Cup at Wembley which earned them qualification for the Europa League next season.
Curtis told The Mirror: "I'm sure we will buy in players in the summer. It's important to do that irrespective of where you finish. There are plans afoot to bring players in.
"We will have to satisfy the players terms-wise, but I would say we'll sign quite a few players. We could sign four, maybe up to six players in the summer if we can."
Swansea are ninth in the Premier League with seven games to play this season.