The 24-year-old defender stepped up amidst an injury crisis last season and made 17 Premier League appearances as he helped Liverpool to finish third in the league.
But Liverpool signed Ibrahima Konate in the summer and the return to fitness of Joe Gomez and Virgil van Dijk means Phillips is the fifth choice centre-back at the club for the moment.
He did not even get a chance to get minutes in the EFL Cup on Tuesday night and Gillespie conceded that the writing is on the wall for Phillips on Merseyside.
He admits that without him Liverpool would not have finished strongly last season, but thinks Phillips himself will already be looking at options to leave given his situation.
Gillespie said on LFC TV after Liverpool’s win at Norwich: “There is somebody out there who will buy Nat Phillips.
“I think we saw exactly what he offered Liverpool and big credit to him for his performances last season because had that not been the case Liverpool would not have finished anywhere near third position in the league.
“He had a big part to play, but that’s the way football is.
“They went and bought a big centre-back in Konate and you have got four top-class individuals ahead of you.
“He probably knows that himself and he is probably looking elsewhere at this moment in time.”
Phillips has made the matchday squad in the Premier League just once and is yet to earn a minute of football this season.