Saints have crashed to home defeats against Swindon, in the Johnstone's Paint Trophy, and Rochdale since the Italian controversially axed Alan Pardew last week.
Supporters sang Pardew's name during Saturday's humiliating 2-0 loss to Dale, and Cortese wants a new man in place ahead of Saturday's league trip to Swindon.
He is thought to favour a young English manager with Nigel Adkins of Scunthorpe and Bournemouth's Eddie Howe emerging as leading contenders.
Exeter boss Paul Tisdale, a former Saints player, has ruled himself out of the running.
Source: PA
