According to Corriere dello Sport, the Argentine rejected a move to the London Stadium last month.
Soule is also alleged to have turned down Crystal Palace and Al-Ittihad.
According to the Italian news outlet, the South American, who is now valued at €30 million (£26 million), wants to continue his loan spell at Frosinone, where he is performing well after signing from Juventus.

According to reports, Soule has no animosity toward West Ham and only wants to take his time before making a decision about his future.

Corriere dello Sport reports that the 20-year-old has decided to depart Juventus at the conclusion of the season, and the Italian club has already signed a replacement in Francisco Martin Barido.
As a result, West Ham may have another opportunity to recruit Soule this summer; it looks that it was more a matter of unfortunate timing than the Argentina U20 international having anything against the Hammers.
If Tim Steiden, West Ham’s Director of Football, can reach an arrangement with Juventus, it appears to be a good commercial deal.

As previously said, Soule is performing admirably in Serie A, with Claudio Ranieri comparing him to Diego Maradona.
Tutto Mercato Web quoted the Italian as stating, “When you have champions like Soule who shoot like Maradona or Zico, you just have to applaud him.” This is a beautiful occasion for those who come to the stadium and pay for their tickets.”
The Mar del Plata-born prodigy has often been compared to Lionel Messi.
Keep an eye on Soule’s status, as West Ham may attempt again this summer.