The Merseyside club have been working on a deal for the Guinean box-to-box dynamo all summer and the Reds' efforts to land the player have caused Leipzig to reconsider their position of refusing to sell.
But with the prospect of Keïta leaving the Red Bull Arena now a possibility, we understand United – along with Manchester City, Juventus and Inter Milan – are also interested in signing the 22-year-old this summer.
Leipzig's public stance remains that they do not want to sell the player, who was signed for £12.75million from sister club Red Bull Salzburg, but there is a confidence inside Anfield that a deal can be done.
The Saxony club's sporting director, Ralf Rangnick, has insisted that none of RBL's star players will be sold this summer as they look to build towards their maiden Champions League campaign. A €65million bid from Liverpool has already been rejected.
But the Reds have received encouragement that an improved offer could see a deal done. And Keita is understood to favour a move to Anfield following the club's pursuit of several months.
United are known to be in the hunt for midfield reinforcements this summer, with Chelsea's Nemaja Matić and Tottenham Hotspur's Eric Dier said to be José Mourinho's top summer targets for the anchorman role.
Keïta, despite misguided comparisons to N'Golo Kanté, is a box-to-box midfielder rather than holding, defensive-minded player.
He scored eight goals and registered seven assists in 31 Bundesliga outings last term and, like the Red Devils' record signing Paul Pogba, the former Salzburg star enjoys the freedom to roam into advanced positions.
However, United were also believed to be targeting Roma's Radja Nainggolan, who is expected to renew his contract at the Stadio Olympic imminently. Although he differs stylistically to Keïta, the two fit a similar positional profile.
In the event of Keïta or a similar midfielder arriving at Old Trafford, Ander Herrera would likely be moved back into the holding role. Although the Spaniard is perhaps a more natural fit for a slightly advanced position, he produced several of his finest performances last season while deputising for Michael Carrick.
Herrera's average of three interceptions per 90 minutes – a return no Premier League midfielder could better in 2016/17 – showed that he has the requisite anticipation skills to break up play at the base of midfield. While the ex-Athletic Bilbao man's 87.6 per cent pass accuracy and six assists demonstrated his ability to conduct play and be creative from deep.
With Pogba on the left and Herrera central, Keïta would theoretically slot into the right side of United‘s midfield three, adding energy, drive and creativity to compliment the gifted Frenchman's skill set.
No Bundesliga central midfielder completed as many dribbles per 90 as Keïta last season (3.1), while his 3.1 interceptions per 90 was better than any United player averaged in the Premier League.
But having entered the race to sign Keïta late in the day, United are firmly behind Liverpool in the running for the 22-year-old's signature.
Arena 11, the player's representatives, enjoy a good working relationship with the Merseysiders having taken Sadio Mané to Anfield from Southampton a year ago.
A source close to the player has also revealed to Football Whispers that, having put so much groundwork into signing him, Keïta is determined to join the Reds: “In his mind, the only possible destination for next season is Liverpool.”
But money talks and United have shown a willingness to splash the cash again this summer, having already spent well in excess of £100million on the signings Victor Lindelöf and former Chelsea transfer target Romelu Lukaku. Ivan Perišić is also reportedly close to a £40million-plus Old Trafford switch.
And Mourinho will be hoping he can snatch another target from under the noses of a rival, just as he did with Lukaku earlier this month.