The Old Trafford hierarchy has already received positive signals from the German's camp as the Borussia Dortmund boss leads the race ahead of Dutch coach Louis Van Gaal.
The Borussia Dortmund manager is United's top choice to take over from the Scot, who is set to be sacked just 11 months after being appointed Sir Alex Ferguson's successor.
|KLOPP EXIT WOULD BE A SURPRISE
|THE VIEW FROM GERMANY
|By Falko Bloeding | Goal Germany
Manchester United would be stupid not to have Jurgen Klopp on their shortlist. But to be honest, the chances of him leaving Dortmund are very, very slim. He has shown absolutely no signs of becoming tired at BVB, and he is as committed as ever.
He signed a new contract until 2018 last October and said at the time: "We are all a little in love with this club and how things are run here. Nothing can separate us and until 2018 nobody needs to call me."
Klopp said last summer that there had been offers, but that he did not want to leave Dortmund: "There were indeed requests. Requests from clubs which I never thought would be interested in signing me and my staff. But my respect towards Borussia Dortmund is so high that I never thought about it."
He's also said in the past that he would only consider leaving Dortmund if he felt the relationship with his team would "change".
That, however, does not look like happening now, or in the immediate future.
Reports also indicate United already has met with Louis Van Gaal, who will be a free agent when he steps down as Holland manager after the World Cup.
However, the meeting, which is believed to have taken place last week, has prompted strong reservations in the United board room about whether Van Gaal's dictatorial management style would get the best out of the players, including the senior core who have been so disaffected under Moyes.
The Scot will be dismissed before Saturday's Premier League clash against Norwich City at Old Trafford, with Ryan Giggs likely to be placed in charge of United until the end of the season. However, the player-coach, 40, is not believed to be a realistic candidate to replace Moyes on a permanent basis because of his lack of managerial experience.
Klopp, who is contracted to Dortmund until 2018, has the greatest appeal to the United hierarchy since he transformed the German club into a European powerhouse after taking over six years ago.
Klopp led Dortmund to consecutive Bundesliga titles in 2011 and 2012, when it also won the domestic double, and was the runner-up in last season's Champions League final.
Dortmund has continued to punch above its weight this season, reaching the quarterfinals of the Champions League only to be narrowly defeated by Real Madrid. It is also second in the Bundesliga table, although a distant second behind recently crowned champions Bayern Munich.
Klopp has been widely linked with a move to the Premier League in recent years but has remained loyal to the club where he has made his name.
United believes it has the prestige and history to turn Klopp's head and bring him to Old Trafford this summer.
The power brokers, led by the Glazer family and executive vice-chairman Ed Woodward, are willing to hand the new man a staggering transfer kitty of up to 200 million pounds to reshape a squad that has failed so dismally this season.