Sources have told ESPN FC that United are interested in central defenders Jerome Boateng, Toby Alderweireld, Harry Maguire and Yerry Mina but Mourinho - who has said the season could be "difficult" if the squad is not bolstered - admitted at a news conference on Thursday he is not expecting any new arrivals.
The pair were asked to pick their Premier League predictions ahead of the new season.
Although there has been speculation about a deal for Tottenham's Toby Alderweireld, there has been no offer from United while Leicester remain determined to retain England worldwide Harry Maguire, who has four years left on his contract.
United have endured a hard summer transfer window as they have tried and failed to sign a host of defensive targets, with Tottenham centre-back Toby Alderweireld and Leicester's Harry Maguire among the names on their wish-list.
'But looking at the squad Jurgen Klopp has assembled, I will be amazed if Liverpool don't push them very, very close.
"My view is that first of all is hard for me to believe we finished second", he added.
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Sky Sports pundit Gary Neville believes that Liverpool need to exit the Champions League early if they have any chance of winning the Premier League this season.
"Is hard for me to understand, to feel, to believe we finish second - which I keep saying, and it is sometimes hard to believe, that I won eight championships and three Premier League's but I keep feeling the second last season was one of my biggest achievements in the game". Mourinho also has selection problems for the Leicester game, with Ander Herrera, Nemanja Matic, Marcos Rojo, Antonio Valencia and Dalot ruled out because of injuries and Paul Pogba, Jesse Lingard, Ashley Young and Marouane Fellaini not considered fully fit after being given extra time off to recover from the World Cup.
Mourinho also needs to check on the fitness of those that returned late from the World Cup.
"The target is Leicester match and the tactics to be changed in Championship Manager you can just press a button", he said.
Pre-season has clearly been a frustrating time for Mourinho, while a perceived lack of respect for leading his side to second spot last term has got under his skin.
'I said during pre-season - it looked like I was saying something absolutely out of order, something insane - but I repeat: pre-season is hard when you don't have your players to work, it's as simple as that'.