The English coach has been in charge of the Swedish club since 2010, during which time he has got them promoted from the fourth tier of Swedish football to the top flight.
In addition, Potter led the modest outfit to the Europa League round of 32 last term, beating Arsenal 2-1 in the second leg at the Emirates Stadium.
According to the Daily Mail, terms are understood to have been agreed with Potter over the switch, but his Swedish employers are yet to strike a deal with Swansea for the 43-year-old.
The report, citing sources at Swansea, claims that the club are confident of move going ahead without any further issues, with Potter set to become the Swans' fifth manager in 19 months.
Carlos Carvalhal departed the Liberty Stadium earlier this month following their relegation from the Premier League.