The 24-year-old left wing-back has been strongly linked with a move to Genoa for several weeks, with transfer journalist Nicolo Schira reporting that the Serie A club are now only details away from completing the signing.
According to Expressen, Hull City are plotting a rival bid for the Swedish international, with the Championship club understood to be preparing an offer of their own. Other unnamed British clubs are also said to be showing interest, according to the report.
Genoa's proposal is reported to be worth €2.2million plus a further €1million in bonuses. Stroud is said to have already agreed personal terms with the Italian club on a contract running until the summer of 2029, with an option for a further year.
Genoa's interest has been building for weeks, with an initial offer of around €1.6million rejected by Mjällby before the Serie A club returned with an improved bid closer to the Swedish champions' valuation.
This season Stroud has scored two goals and provided one assist in eight league appearances, seven of them starts, for the reigning Allsvenskan champions. He impressed at the World Cup in the United States over the summer, starting for Sweden against both Japan and France before their exit at the last-32 stage, and has previously turned down interest from three Championship clubs in favour of waiting for a move to Italy, a stance that underlines his stated preference for Serie A over an immediate switch to English football.
Since joining from Oddevold in 2023, Stroud has made 104 competitive appearances for Mjällby, scoring 24 goals and registering 14 assists, and has won both the Allsvenskan title and the Swedish Cup with the club.
His contract with Mjällby runs until the end of 2026, meaning the Swedish club retain some leverage but also an incentive to sell this summer rather than risk losing him for a reduced fee, or for nothing, further down the line.