The Eagles recently drew 1-1 with Everton at Goodison Park.
The Eagles are flying under Alan Pardew, and are currently sixth in the table with 23 points from 15 games.
That tally leaves them just three points behind Tottenham Hotspur in fifth and only six behind Manchester United and Manchester United in third and fourth.
They are firmly in the race for a European spot at this stage of the season, and Parlour has backed them to remain in the hunt for the remainder of the 2015/16 campaign.
“Palace are going really well, they’re sixth in the league,” he told TalkSport.
“I had Palace to come in the top ten at the beginning of the season. Can they keep it going? I’m sure they can. Alan Pardew has got some good players down there. It was a good point the other night against Everton.”
If Palace are to try and challenge for a place in Europe this season, they will be heavily reliant on key duo Yannick Bolasie and Yohan Cabaye.
Those two are currently their top goal scorers in the league with four apiece, with defender Scott Dann the closest behind them with three league goals.
That means losing either player would be a huge blow, with the goals not flowing freely from anyone else, especially the strikers, with Dwight Gayle, Fraizer Campbell, Connor Wickham and Marouane Chamakh yet to score in the league.