The 17-year-old has been a breakout for Mexico, becoming the youngest player to ever represent the nation at a World Cup.
According to TEAMtalk, Liverpool have registered a "serious interest" in securing the services of Mora from Club Tijuana.
While Liverpool are moving to secure an early advantage over potential rivals, they still face serious competition from other top European clubs.
It’s understood that Real Madrid are right there beside Liverpool in the race to sign Mora, with Barcelona, Manchester City, Chelsea, and Arsenal also keen.
Rivals Man United have pulled out of the race, however, despite having scouted the young playmaker for the past six months.
It’s understood that Club Tijuana currently value Mora at around €40 million (£34m).