The Nigeria U23 international is on a season-long deal with the German Second Division outfit and is beginning to impress.
Awoniyi has featured in the past six league games for FSV - and scored his first goal for the club against Heidenheim last Friday.
FSV chief Clemens Kruger says the Nigerian is now benefiting from being played in his natural striker's role.
"Taiwo Awoniyi is a striker, during the last games he's played in his regular position," Krüger told Tribalfootball.com.
As for next season, Kruger admits there's plans to sit down with Liverpool and discuss extending Awoniyi's stay.
"Taiwo is a highly promising player with great potential and his whole career ahead of him. In late summer, 2016 he will participate in the Olympic Games in Rio de Janeiro with the national under 23 team of Nigeria. Of course we would like to extend the agreement with Liverpool FC.
"We will discuss that in time," added Kruger.