Her official spokeswoman said: 'We would certainly like to host a reception for the England football team, who did so well in Russian Federation, and that is something that we are going to talk to the FA about'.
Wednesday's audience peaked between 21:30-21:35 BST as England tried to find an equaliser at the end of extra time in the semi-final against Croatia.
"It was a tough game, a 50-50 game, I'm sure we'll look back at stuff we could have done better but we worked as hard as we could. Thank you all for your support!" We have proved to ourselves and our country that it is possible.
"There'll be a new benchmark and level of expectation", said Southgate.
"I'm remarkably proud of the group of players", he added.
England captain Harry Kane - who has six goals in the tournament ahead of Saturday's third-fourth place play-off against Belgium in Russian Federation, said: "It's been an awesome run but it hurts to lose, it really hurts".
Croatia will now take on France on Sunday in the final, while England shall battle Belgium in the third place play-off.
"We played well at the start and in extra time but we missed a few chances to kill them off".
'The players have to look at the reaction of the supporters and see. We will want to give a performance of huge pride.
"But I've said all along we're not flawless, we're not the finished article".
In the knockouts, they needed penalties to get past a Colombia team shorn of their top player, James Rodriguez, and then beat Sweden with two headers and with keeper Jordan Pickford making some crucial saves.
Commenting on the calls earlier today, Mrs May's spokeswoman said: 'She obviously thinks he led the team fantastically.
"We've created good chances in pretty much every that game we've played, and the strength in set-plays was something that we put a focus on because we knew the importance of it, so for me that's been a positive rather than a negative".
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