Frank de Boer and Mauricio Pellegrino are among the names on the shortlist to replace Claude Puel as Southampton manager, Press Association Sport reports.
Despite guiding Saints to eighth in the Premier League and the EFL Cup final in his first season, frustrations behind the scenes and in the stands led to the end of Puel's reign on Wednesday evening.
Southampton are looking for a manager with a shared "long-term vision" after sacking Puel, and De Boer and Pellegrino are reported to be among their possible targets.
Former Borussia Dortmund manager Thomas Tuchel was on the long list of potential candidates but is not reported to be on Saints' final list. Sky Sports News has reported that Tuchel, who was the early favourite with bookmakers, is not interested in the job.
Ex-Bayer Leverkusen coach Roger Schmidt was of interest but has joined Beijing Guoan, while Marco Silva has already switched Hull for Watford.
Southampton have shown a preference in recent years to appoint managers out of work, as seen with Mauricio Pochettino, Ronald Koeman and Puel.
De Boer has been without a job since a short, frustrating stint at Inter Milan came to an end in November.
The former Ajax boss had been under consideration by Saints last summer, but at that time there was an apparent reluctance to appoint another Dutch coach after Koeman's exit.
Pellegrino led Alaves to the Copa del Rey final in his only campaign at the helm after spells in charge of Valencia, Independiente and Estudiantes. The former Argentina international coached under Rafael Benitez at Liverpool and Inter Milan.
The new manager will not only arrive at Southampton with a Chinese takeover hanging overhead, but also with continuing questions about key players.
Rumours continue to circle around Virgil van Dijk, despite Liverpool pulling out of the race to sign the defender. Ryan Bertrand, Oriol Romeu and Dusan Tadic are among others to be linked with a St Mary's exit.