Former Reds captain Steven Gerrard was indirectly responsible for Alli's move to Tottenham Hotspur instead.
Alli has starred for club and country this season - his first outside the third tier of English football - though it should have been Liverpool benefitting from the 19-year-old's ability, according to Hughes.
The report states that Alli required little convincing over a move to Anfield, where his former manager Karl Robinson, a Reds supporter, began his coaching career and his hero Steven Gerrard was playing at the time.
The former MK Dons midfielder is said to have received a guided tour of Liverpool's Melwood training complex, however the club never thought it wise to introduce him to their then captain, who was sleeping ahead of a big game.
For months nothing came of Alli's trip to Merseyside, claims Hughes, with Liverpool unwilling to meet the Dons' asking price until a £3 million deal was struck in November 2014.
It is said that at this point someone at Anfield decided to try and negotiate the club and player down by half - tying in with this report from The Mail in February - which led to an impasse.
Mauricio Pochettino, the Tottenham head coach, apparently realised that Liverpool were ahead of Spurs in the queue for Alli but took advantage of the situation by making his signing a priority.
In the end, the north London side agreed to pay £2 million more than the fee initially agreed with Liverpool in order to land the teenager, and it looks to be a bargain so far.