According to the Scottish Sun, the Reds have seen an offer worth approximately £200,000 ($285, 270) accepted for the 18-year-old left-back, with add-ons and a sell-on clause also set to be included in the deal.
Liverpool moved quickly to secure the capture of Gallacher, who spent time on trial at their Kirkby Academy earlier this month and will initially join up with Neil Critchley's Under-23 squad, potentially in time for their latest Premier League 2 clash with Derby County at Tranmere Rovers' Prenton Park on Sunday (28 January).
United, Stoke City and Swansea City, along with Old Firm duo Celtic and Rangers, were among the other teams to have recently scouted the former Scotland Under-17 international, per the Falkirk Herald, after he rose through the youth ranks in Stirlingshire to make his senior debut as a 16-year-old in the Scottish Cup victory over Fraserburgh in November 2015.
Gallacher has made a further 25 appearances since then, drawing additional attention from the likes of Chelsea, Manchester City, Arsenal, Everton and even La Liga giants Barcelona, who were said to have made a surprise check on his progress at this time last year.
Neither Falkirk nor Liverpool have yet publicly confirmed an agreement for the latter's low-key second January signing to follow the record £75m capture of centre-back Virgil van Dijk from Southampton, with the Bairns first announcing the arrival of third-string Celtic goalkeeper Conor Hazard on a six-month loan deal.
Gallacher will strengthen a Liverpool Under-23 team that have been weakened by several departures in January, with Cameron Brannagan offloaded to Oxford United and Corey Whelan and Matty Virtue loaned out to Yeovil Town and Notts County respectively.
Critchley, who is also without Rhian Brewster after the gifted striker was stretchered off with a serious ankle injury in the 3-2 defeat to City on 12 January, recently claimed that further exits were possible - with Harry Wilson, Ovie Ejaria and Lloyd Jones among those who could also be dispatched to gain first-team experience in the Football League.
"More loans is a possibility," he told the Liverpool Echo. "You look at Harry, Ovie and we still have Lloyd with us at the moment. They would be the three who would come under the radar of other clubs.
"There are lots of variables. What happens at first-team level will have an impact on who stays and who goes. If they go on loan brilliant, if they don't and they keep playing well here they will be knocking on the door.
"They are in a good situation at the moment. There is no rush for them. We'll see what happens over the next week."