The winger has impressed at the beginning of the Championship season.
The Reds have been busy this summer, with seven new faces arriving at Anfield so far.
Most of their signings have been first team ready players as Jurgen Klopp has tried to build a side capable of an assault on the top four this season.
Nottingham Forest's Oliver Burke shoots at goal
He has also shown his desire to plan for the future though, with signings such as Marko Grujic, and to some extent Loris Karius, very much ones for the future.
The young winger broke through into the Reds first team last season, making 18 appearances across the campaign and scoring two goals.
Watford's Adlene Guedioura in action with Nottingham Forest's Oliver Burke
He has also started this season strongly, starring in their win over Burton Albion and also putting in a top display in the defeat to Brighton and Hove Albion.
If Klopp’s side are interested they will have to move quickly though, with the report claiming Crystal Palace are eyeing the player as a direct replacement for Yannick Bolasie.
Crystal Palace manager Alan Pardew