The 22-year-old is expected to complete the switch to the English Championship from Borussia Monchengladbach side this week.
A deal is all but agreed after visa issues were ironed out, Wales Online report.
Wolf, a one-time €12million signing for RB Leipzig, has fallen out of favour with his current club.
Monchengladbach’s sporting director recently confirmed “something might happen in the next few days” with regards to Wolf leaving the club.
Wolf, who has yet to make his debut for Austria, will link up with former Rangers defender Russell Martin who is in charge of Swansea.
The Welsh side are 17th in the English Championship.
Wolf can operate in a variety of attacking positions and will be looking to rediscover the form he showed breaking through at Red Bull Salzburg.