The Reds are top of the table after six games, two points ahead of Chelsea and defending champions Manchester City.
Jurgen Klopps side seem primed to launch a serious title bid, with just two goals conceded in six games and a star studded attacking line.
But Moyes, a former Manchester United and Everton manager, is not backing the Reds to finally lift a Premier League trophy this season.
No, I dont think so, Moyes told Sky Sports when asked if Liverpool could win the title.
I think theyve got a really good team, but you look back at teams over the years at Liverpool and they had great teams, when it was (Xabi) Alonso, (Javier) Mascherano, (Steven) Gerrard and (Fernando) Torres up front.
This is a good Liverpool team as well – I dont know if its quite as good as that team at that time. Theyre playing a good style, with forward players who are exceptional, and because of that I think theyre a real threat.
The Rafael Benitez side that boasted Xabi Alonso, Javier Mascherano, Steven Gerrard and Fernando Torres finished second in the 2008/09 season, four points behind winners United, but the following campaign plummeted to seventh place.
While Liverpool were a formidable force going forward last season, Klopp seems to have finally solved their defensive failings by bringing in goalkeeper Alisson and centre-back Virgil van Dijk in the last nine months.
The Reds begin a double header against Chelsea on Wednesday, before a crucial game against Manchester City at Anfield on 7 October.