The 19-year-old midfielder has attracted interest from a number of clubs in England and is currently on trial with the Saints.
Gbadehan has been looking to make an impression on Southampton and it appears he has succeeded.
Russell Martin’s side are expected to play Gbadehan in a behind-closed doors friendly on Wednesday to take a further look at him.
The American, who has a British passport, was on trial at Brentford last week, but it is Southampton who appear set to sign him.
He played for Future SC Monarchs, a Maryland-based American academy, for whom he won the Dallas Cup in 2021.
However, Gbadehan did not decide to stay in the United States with an MLS-affiliated academy, preferring to try his luck in Europe.
Gbadehan will hope he can quickly make an impression at Southampton if he does put pen to paper to a contract at the Championship club.