The Swedish club value the 24-year-old at around €2.6million, but he has just five months remaining on his contract with Mjallby and is understood to be keen to leave Sweden to try his hand in Italian football.
Stroud, who was born in Uddevalla and began his career at IK Oddevold before joining Mjallby in 2023, has recently broken into the Sweden national team, receiving his first senior call-up in March for World Cup qualifiers against Ukraine and Poland.
He can play at left-back or on the left of midfield, and his combination of pace and crossing ability has made him one of the more sought-after Swedish exports of the summer.
Genoa's move for Stroud comes as the club also confirmed the departure of a young academy player in the opposite direction.
According to TMW, Juventus have completed the paperwork to sign Raffaele Aresini on a permanent basis after a season on loan at the Turin club.
The 17-year-old left winger arrived at Juventus last summer from Genoa on a loan deal with an option to buy, and impressed at Under-17 level, reaching the final of his age-group competition before losing out to Empoli.
Juventus have now exercised that option, tying Aresini to a three-year contract and confirming their faith in one of the more promising talents to come through Genoa's youth ranks in recent seasons.
The Rossoblu will hope Stroud can prove an equally shrewd addition at first-team level, with the Swede offering both physicality and Serie A ambition as Genoa look to strengthen their options on the left side of defence this summer.