Wednesday 29 June 2016 15:02, UK
Matt Le Tissier believes it would be too big a risk for England to appoint an interim manager to replace Roy Hodgson.
Hodgson resigned after England's 2-1 defeat by Iceland in the last 16 of Euro 2016 on Monday, meaning they still haven't reached the semi-final of a major tournament since 1996.
FA chief executive Martin Glenn says they will look "globally" for a successor and while Southgate is open to taking charge on a temporary basis, according to Sky sources, Le Tissier says that would be the wrong move.
He told Sky Sports News HQ: "The England job is too important to be put in the hands of a caretaker. If you're going to make a decision you have to make it now.
"We have World Cup qualifiers coming up and I think it would be a big risk to give it to a caretaker manager.
"The list of names I've seen this morning isn't particularly compelling if I'm honest. There's no one candidate that stands out above all others.
"If you're looking for an English manager then you've got the likes of Eddie Howe, Sam Allardyce, Alan Pardew, but you need the best man for the job now.
"Martin Glenn says we'll be looking globally for the best man, and if you want England to be successful, that's what we need."
England have only had two foreign managers in the national team's history; Sven Goran Eriksson between 2001 and 2006, and Fabio Capello between 2008 and 2012.
Arsenal manager Arsene Wenger is among the bookies' tips to be approached for the job, but Le Tissier is adamant the Frenchman would miss the pace of club management.
Le Tissier said: "I'd be very surprised if it was Arsene Wenger if I'm honest, he's got a fantastic job at Arsenal and a job for life, we've seen that.
"Would he really want to put himself in that position as England manager with all the pressures that come with it? I'm not sure.
"I think he's one of those guys that seems to enjoy and relish the day-to-day involvement of football, and I think he'd miss that as an international manager.
"You need the best man for the job now. We've gone down the route of foreign before, we've now gone down the English route, and neither has worked."