The 19-year-old full-back, who made 12 appearances last term, committed his future to Liverpool by signing a long-term deal last summer.
This season, Alexander-Arnold has made 27 appearances in all competitions, his swift progress being hailed by manager Jurgen Klopp.
According to The Mirror, Liverpool had already planned to offer Alexander-Arnold a wage boost even before his impressive performances in the Champions League quarter-finals against Manchester City.
The report goes on to claim that talks will take place in the summer to fast-track the defender onto a better deal after making huge strides this season.
In addition, Alexander-Arnold is believed to be in serious contention for a place in Gareth Southgate's England World Cup team.