West Ham United are currently one point away from the Champions League qualification spots.
As things stand, Slaven Bilic’s side are just one point away from the Champions League qualification spaces.
However, Parlour does not feel that Manchester City or Arsenal will slip up - and he believes West Ham will have to settle for a Europa League qualification spot.
“I look at the top four, and it is whether they’ll slip up. I don’t think they will,” he said.
“I think West Ham and Manchester United could finish where they are now - fifth and sixth.
“That’s a fantastic season for West Ham.”
West Ham won their last match 3-2 against Everton in very dramatic fashion to keep up their push for a top four spot.
The Hammers were 2-0 down at Goodison Park, before they staged an unlikely comeback.
Michail Antonio, Diafra Sakho and Dimitri Payet all scored for the Hammers in the last 11 minutes, as they secured the three points.
West Ham have now won their last four matches in succession, and their next fixture comes against Manchester United in the FA Cup.