The Reds are in ninth place and nine points behind fourth-placed Manchester City after Manuel Pellegrini’s side were 4-0 winners against Aston Villa on Saturday.
Another three points would maybe signal to more and more people that we can still get to that Champions League place
Jurgen Klopp’s side, who were 3-0 winners against City at Anfield mid-week, can close the gap to six points when the Reds take on Crystal Palace at Selhurst Park on Sunday afternoon.
Former Liverpool striker Mellor, who helped the Merseyside outfit to win the Champions League in 2005, believes Klopp’s players still have an outside chance of a top-four finish.
“Top four is still a big ask – but it’s possible now,” Mellor told Liverpool Echo.
“We have hope and with more results like Wednesday’s and by adding that vital bit of consistency, we can stay in the hunt.
“Obviously that starts at Crystal Palace on Sunday.
“They are struggling pretty badly just now and while it hasn’t been our happiest hunting ground recently, we’ve got to go and take advantage of their woes.
“Another three points would maybe signal to more and more people that we can still get to that Champions League place. Going into a great double header against United in the Europa League, it would also give us some real momentum.
“We’ll see if it all happens.
“But if it does, we might just look back at the midweek win over City and say that was where a new chapter began.”
Liverpool have a miserable record against Palace in recent seasons after a run of three defeats in their last four meetings in all competitions.
Alan Pardew’s Palace side haven’t won a Premier League game since 19 December when the Eagles were 2-1 winners at Stoke City.
Palace are 15th in the table and eight points above the relegation zone.
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