Saints have reportedly been refused permission to speak to Fulham manager Felix Magath.
Saints have already held talks with Ronald Koeman, who is leaving Feyenoord this summer, but they intend to speak with other candidates before making a final decision.
An appointment is likely to be made towards the end of next week, or the beginning of the following week.
German manager Magath joined Fulham on an 18-month contract in February, but was unable to keep them in the top flight.
The 60-year-old, who has managed clubs such as Bayern Munich, Werder Bremen and Schalke, has already said he remains committed to staying at Fulham, despite the team’s demotion to the Championship.