Wednesday night's game was England's first semi-final in 28 years, after the 1990 squad were defeated by West Germany in a penalty shoot-out.
Her 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".
England Football Tweeted to their fans to thank them for support throughout the Russian Federation 2018 campaign.
England have been eliminated from the World Cup right at the penultimate stage, and Croatia are now through to Sunday's finals instead.
"It's a young team, the majority of the players will play in the next World Cup with more experience at club level", the Portuguese boss told RT.
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Numbers have also seemingly been kept down by diplomatic tensions over the poisoning of a Russian former double-agent and his daughter in Salisbury in March, and now the death of a woman who police say was poisoned with the same nerve agent. "Everyone is born with it, we have good players, and I believe they will bring the cup home, but we'll see on Monday morning at 3 o'clock". We're all feeling it.
In central Moscow one England fan climbed up a lamp post to lead chants from England supporters before the match.
There was a heavier police presence than usual, though police were relaxed and three officers chatted and laughed with England fans.
"Then they play a team in Sweden who were in awe of England".
"I want to emphasise the midfield", Souness explained to beIn Sport after the game.
Jordan Pickford starred yet again between the sticks for England and the goalkeeper was pictured in conversation with his fiancée Megan Davison.
England fans in London react to key match moments in the World Cup semifinal loss to Croatia.