Emery, who was unveiled as Arsene Wenger’s successor in north London earlier this week, says his end goal is to take Arsenal back to the top and challenge the likes of City.
However, the former Sevilla and Paris St Germain boss will have to work on a limited budget in his first summer at the club.
And former Gunner Parlour says without similar funds to the Premier League champions, the title is out of reach.
“I would love him to do it [win the title], but I’m going to say no,” Parlour told Talksport.
“I think Man City are going to get stronger and stronger, and I think Pep Guardiola is going to stick around.
“I can’t see who’s going to challenge them.
“Top four is going to be important [for Arsenal]. They’ve got to get back into the Champions League, so, for me, top four will be a very successful season.
“Unless there’s massive investment, the same as at Man City, [they’ll never win the league].
“Man City will go out and buy the big players. If Pep Guardiola stays around and they keep trying to make the squad better, it’s going to be very difficult.”