The Reds are currently seventh in the Premier League table heading into their final 10 games of the campaign under new boss Jurgen Klopp.
Liverpool are six points behind fourth-placed Manchester City as the race for Champions League qualification hots up.
However, former Reds defender Jones does not believe that Klopp’s side have what it takes to climb up the table and finish fourth this season.
Speaking exclusively to The Sport Review, Jones said: “I don’t think so [Liverpool can finish in the top four].
“We’d need to put a big run together until the end of the season and see what happens. It is going to be difficult.
“All you can do is hope some other teams slip up and we sneak in.”
Liverpool’s next Premier League game is a trip to St Mary’s to face Southampton on Sunday 20 March.
The Reds finished sixth last season under Brendan Rodgers, before the Northern Irishman was sacked and replaced by Klopp back in October.
Liverpool take on Manchester United in the return leg of their Europa League last-16 clash at Old Trafford next Thursday.
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