Southampton have given themselves a 10-day deadline to appoint their new manager, the Daily Echo reports.
Les Reeds hopes to have a new man at the helm ready for when the players return for pre-season training on 29 June.
A whole host of names have been linked with the vacant post since the Saints parted company with Claude Puel at the end of the season.
Frank de Boer and Mauricio Pellegrino are the two front runners for the job after former Borussia Dortmund man Thomas Tuchel admitted he was not interested in taking over from Puel.
Other names to be linked include Roberto Martinez and Roger Schmidt, who took a job in the Chinese Super League.
Hoffenheim boss Julian Nagelsmann had emerged as a target for Southampton, but the Saints are unlikely to be able to lure him away from the Bundesliga after he guided the German side into the Champions League at the age of just 29.