According to 'Sportsmail', talks with Ostersunds boss Graham Potter are reaching a conclusion, although the appointment is unlikely to be confirmed until after the weekend.
Potter has been at the helm of the Swedish club since 2011, but is set to bid farewell in favour of a move to Wales. Swans will need a smooth transition as they seek to earn promotion back to the Premier League.
Swansea have long held a relationship with Potter, and he has been hugely successful with Ostersunds having earned them three promotions in five years and led them into the Swedish top-flight.
Other potential candidates for the top job include former Reading manager Jaap Stam and ex-Inter and Ajax boss Frank de Boer.