At right-back, the likes of Kieran Trippier and Max Aarons have been linked amid their fine performances for Atletico Madrid and Norwich City respectively.
For the centre-back position, Raphael Varane, Jules Kounde and Ben White are all names under consideration.
And, up top, United are determined to win the race for Erling Haaland despite the likes of Chelsea, Real Madrid, Barcelona and Manchester City also being admirers of the Borussia Dortmund star.
Meanwhile, speaking last month, West Ham boss David Moyes insisted the club would be entitled to demand £100million for Rice due to his importance to the side.
“I don’t agree with the owners that Declan Rice is a £100m footballer. Far, far more than £100m. Far, far more,” said the Scot.
“I look at the players who have joined some clubs from overseas and come in and nowhere near had the impact Declan Rice would have.