The 22-year-old has just enjoyed a productive loan spell at Sheffield United, contributing 12 goals and 10 assists from 37 appearances in the Championship.
Wolves head coach Bruno Lage is keen to include Gibbs-White in his first-team squad next season, while the club want to extend his contract past 2024.
However, the England Under-21 international is naturally attracting interest from elsewhere, speculation emerging earlier this month that AC Milan have taken note of his performances.
According to The Sun, Southampton are now admirers of the playmaker and would be prepared to sign him for a fee in the region of £20m this summer.
The Saints need to refresh their squad after only collecting 40 points from their 38 top-flight fixtures this campaign.
Such a figure may be enough to tempt Wolves into a sale, although selling a homegrown talent to a potential rival would divide opinion among the club's fanbase.