Swansea are keen to have a new management team in place before they return to action after the international break, with their next game at Bristol City on Saturday, 22 November.
Hellberg has been in charge at Hammarby for the past two seasons and has led the Stockholm club to successive second-placed finishes in the Allsvenskan, Sweden’s highest division.
He has a year to run on his current Hammarby deal, meaning Swansea would have to pay a compensation fee to secure his services. However, the size of the fee is not likely to be an issue for the Welsh club.
Hellberg was in contention for a move to Wales after the departure of Luke Williams in February, only for Sheehan to land a three-year contract on the back of a sharp upturn in form at the back-end of last season.
Hellberg, who spent his playing career in the Swedish lower leagues, began his coaching career more than a decade ago.
He made his mark as a coach in the lower divisions with Kuddby IF and then IF Sylvia before joining the staff at top-tier club IFK Norkopping in 2020.
Hellberg’s first head coach role in the Allsvenskan came at IFK Varnamo, where two impressive seasons led to his move to Hammarby.
