In reports cited by The Daily Star, it is claimed that the Reds began discussions over the 18-year-old earlier this week, with Brendan Rodgers supposedly willing to pay an initial £3.5 million for his services.
The same source - which claims Alli has also attracted attention from Chelsea, Manchester and Arsenal in recent months - further claims that such a price could eventually rise to £8 million.
If such speculation - along with Liverpool's reportedly imminent bid for Schalke starlet Max Meyer - does indeed prove to be accurate, then it would appear that Brendan Rodgers may well be prioritising the addition of promising young attacking talents to his squad during the early stages of the summer transfer window.
This will perhaps not come as much of a surprise, particularly given Rodgers' history as an accomplished youth coach with Championship outfit Reading and indeed under Jose Mourinho at Chelsea.
While Alli is perhaps not yet totally ready to make a sizeable impact and stake a claim for a first-team place at Anfield, his exciting and eye-catching performances at Stadium mk would suggest that he has the potential to progress to the stage where he can compete sufficiently at a far higher level.
Liverpool fans - who appeared to grow extremely fond of Rodgers during what was an excellent 2013/14 campaign for the club - will be hoping that negotiations for Alli will progress at a relatively rapid rate so the Northern Irishman can move to to attempting to strengthen unquestionably the weakest area of his current squad - the defence.
For all of Liverpool's extremely impressive attacking displays last season, their backline rarely looked capable of carrying the side over the line to to an unlikely title triumph.
With doubts surrounding the future of stalwart Daniel Agger, the likes of Kolo Toure and Mamdou Sakho having often flattered to deceive and Luis Enrique having been sidelined for the majority of the year, Rodgers will need to ensure that he is able to find significant upgrades both in the centre of defence and at full-back.
The likes of Meyer and Alli would be a satisfying start to a busy window for Liverpool, but there are surely bigger deals to come.