For large parts of the summer window, the Premier League giants failed to add a single player to Arne Slot's first-team squad.
Versatile attacker Federico Chiesa was eventually signed after a deal was agreed for Valencia goalkeeper Giorgi Mamardashvili to join in 2025.
Liverpool have shaken off the lack of incomings to win their first three Premier League fixtures of the season without conceding a goal.
However, there was speculation that they made an attempt to secure the signature of Huerta before the August 30 deadline.
Huerta confirms Liverpool interest
Prior to the international break, Pumas manager Gustavo Lema admitted that he would have been proud to see Huerta link up with the Merseyside outfit.
A total of 17 goals and 11 assists from 75 outings for Pumas has led to the 23-year-old becoming a 10-cap international with Mexico.
Huerta, who can play across the forward line, will be focused on starring for Pumas after returning from his time with Mexico, who he represented in a goalless draw with Canada on Tuesday night.
Nevertheless, he says that he remains confident of eventually sealing a transfer to Liverpool or, at the very least, a high-profile European club.
As quoted by AS, Huerta said: "I already had my suitcase ready, and I dropped it. I know that sooner or later, if I keep doing things right, I'll get the opportunity. It's a train that only happens once and I'm focused on Pumas.
"I come to the national team, and I try to do my best to help my team. I know the rest will come soon."
Would Sunderland still be a factor?
When speculation persisted earlier in the summer, it was suggested that Sunderland were the reason why a transfer failed to materialise.
The Black Cats, who currently top the Championship standings, opted against accepting the chance to sign Huerta on loan had he signed for Liverpool.
Unless there is a change of stance, an alternative team would need to be identified if the playmaker was to move elsewhere on a temporary basis.