Arsenal booked a Europa League semi-final date with Valencia after a 1-0 victory in Naples on Thursday.
The Gunners sealed a 3-0 aggregate quarter-final success over Napoli, with Emery continuing his fine record in a competition he has already won three times with Sevilla.
Their home form in the Premier League has also lifted Arsenal back into the top four with five games still to play and, speaking on The Debate, Parlour is impressed with the instant progress the club have been making.
“I did not expect Arsenal to be in the top four at this stage of the season,” Parlour said. “With a new manager coming in there were lots of changes, but if they finish fourth it has to go down as a remarkable season.
“I had them down to finish fifth or sixth, then they could build on that next season, but at the moment they are in a very good position.
“Valencia won’t be an easy semi-final, but Emery has a great record in the competition and plays a really strong team every time. They have a real chance of winning it.
“Emery also knows, like Manchester United did a few years ago, winning the Europa League is an avenue into the Champions League, which is so important for the club, having not been in it for the past two or three seasons.
“Financially they have missed out, and have also missed out on players, because players want to play in the Champions League.”
Chelsea also booked a spot in the semi-final after a 5-3 aggregate success over Slavia Prague, with Eintracht Frankfurt their opponents in the semi-final, before what could be an all-English affair in the final.
Former Chelsea midfielder Steve Sidwell believes that, contrary to Arsenal giving Emery time to improve his side, Chelsea’s hierarchy have a rather different outlook when it comes to what is expected.
“What comes with the territory with Chelsea is that they need instant success”, Sidwell said. ” Whether that is finishing in the top four, or winning the Europa League – Chelsea cannot have another season without Champions League football.
“That has been the case for managers before, and it is the case for [Maurizio Sarri] now, especially with the money involved. Arsenal were not expected to get into the top four, but Chelsea have to.”