United are on the hunt for a new permanent boss after sacking Jose Mourinho just before Christmas.
Red Devils hero Ole Gunnar Solskjaer has taken caretaker charge at Old Trafford and won his first five games.
He takes his Manchester United side to Tottenham on Sunday in a crunch clash as United chase a spot in the Premier League top four.
It is understood that Spurs boss Mauricio Pochettino is United’s No 1 choice to be the next permanent manager.
But the Telegraph now report that England boss Southgate has been added to United’s shortlist amid fears over whether Pochettino will make the switch.
Southgate signed a new contract with the Football Association in October that keeps him as England boss until the 2022 World Cup.
And it’s claimed that could be problematic for United, who tried to appoint former Three Lions gaffer Sven Goran Eriksson in 2002.
Former Real Madrid boss Zinedine Zidane is also on United’s shortlist having been without a club in the summer though there’s been suggestions that he may not suit Old Trafford.
Southgate could be tempted though, despite having had just one club managerial role.
That came with Middlesbrough where he was boss for three years between 2006 and 2009.
But Southgate has had success with the national team, taking England to the World Cup semi-finals in Russia for the first time since 1990.
United have been forced to explore other possibilities to Pochettino following rumours that he will not leave Tottenham.
The Sun recently claimed that Spurs chairman Daniel Levy will block Pochettino’s move even if United offer £50million for his services.
Pundit Danny Mills recently backed United to go after Southgate.
“I tell you whose name hasn’t been thrown into this – Gareth Southgate,” Mills said.
“If I was Manchester United, who would I want as my next permanent manager?
“I’d want a feel-good factor, someone to bring through young players, somebody that plays in the right way, somebody that can connect and reconnect with the fans all over the world.
“I’m not sure he would want the job, and I’m not sure they could get him.
“But surely he’d have to come into the reckoning if you’re Manchester United.
“If I was Manchester United, you might not get Pochettino out of Tottenham.
“He’s got a long-term contract there and he’s now going into a new stadium.
“So you might not be able to get him, even at the end of the season.
“I just think [Southgate] is a name that is out there. Look at how well he’s done.
“He’s just got Coach of the Year, is that the sort of person Manchester United need?”