Emery, 46, is expected to be confirmed as Arsenal’s new manager in the coming days.
Express Sport understands the appointment will be revealed, with a press conference planned for later in the week.
Emery was sacked by PSG this month despite leading the club to a domestic treble.
He had an open chequebook in Paris and spent £200m bringing Neymar to the Parc des Princes from Barcelona.
And Arsenal icon Wright has warned the Spaniard he will have to be wise with his £50m summer transfer kitty in north London.
“Emery has had loads of money to spend at Paris Saint-Germain,” he said on 5 Live.
“Now he has to come to Arsenal with £50m with a bunch of players who have been playing in second gear.
“His coaching ability will have to get going instantly and he will have to find some gems instantly.”
Arsenal are working on transfer deals, with the window having opened last Thursday.
They had wanted a manager in place to replace Arsene Wenger before the World Cup.
Mikel Arteta was interviewed for the job but the former Gunners captain is said to have been put off by Arsenal’s relatively small transfer budget.