BBC Sport
Boro are second in the table, five points behind Coventry City.
Hellberg, who spent his playing career in the Swedish lower leagues, has a year to run on his Hammarby contract.
He began his coaching career in the Swedish lower divisions with Kuddby IF, moving to IF Sylvia before joining the staff at top-tier club IFK Norrkoping in 2020.
His first head coach’s role in the Allsvenskan came at IFK Varnamo, where two impressive seasons led to his move to Hammarby.