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Rice was very impressive in West Ham's 1-0 defeat against United at Old Trafford last night and was in conversation with England teammate Maguire after the final whistle.
The pair put their hands over their mouths, as often players do these days, before United boss Solskjaer joined in and the three of them were seen laughing.
Maguire finished by ruffling the West Ham vice captain's hair and plenty of United fans joked the whole sequence was their skipper and manager "tapping up" Rice - a reported target for the Red Devils.
You might remember Solskjaer was heard telling Nathan Ake, "We need a left footed centre-back, keep going," after a 5-2 win over Bournemouth in July - though the Dutchman signed for rivals Manchester City instead.
Rice, who can play in midfield and as a centre-back, has been progressing very well at West Ham and attracting interest from a number of the Premier League's top clubs.
And former United midfielder Owen Hargreaves believes he's a perfect fit for United.
"I think Rice's upside is off the charts," the former England man told Premier League
"He has the potential to be anything and a lot better... I think he plays within himself at West Ham.
"People don't realise how big he is... he's 6ft 3in, so he looks like a centre back but he's actually really good technically.
"I'm not a big fan of players who just play in there and pass it around, you have to stop players too.
"Declan Rice doesn't have to dictate the game for Man Utd, he can pass to the players who can make the difference and be good defensively."
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