The club's future has been uncertain since former owner Markus Liebherr died in August and in December it was reported that the club would be sold.
Southampton are refusing to make an official comment on the speculation.
Markus Liebherr rescued the Saints from administration when he bought the club for about ?14m in July 2009.
When the Swiss billionaire died last summer, his daughter Katharina Liebherr took control of the club, and chairman Nicola Cortese was quick to reassure Saints fans the club was not for sale.
Source: BBC Sport
Source: BBC Sport