Arsenal and Lille have agreed a £72million fee for 24-year-old winger Pepe.
The Ivorian was the second top scorer in Ligue 1 last season, scoring 22 goals in 38 appearances.
The deal is set to smash Arsenal’s transfer record, overtaking the £56m they paid for Pierre-Emerick Aubameyang in January 2018.
Arsenal’s owners, headed by Stan Kroenke and son Josh, have often been criticised for not spending enough by supporters.
Josh Kroenke, who is a director, claimed in an interview earlier this month supporters should be excited about the club’s future transfer dealigns.
And now White says, with Pepe set to sign, it is time the Gunners fans thanked their owners.
“We were quick to have a pop at Josh Kroenke the other day on this very show when he said ‘be excited’,” White said on talkSPORT.
“We played the audio and we said ‘yeah, yeah, yeah, we’ve heard it, be excited about what?’. Be excited about this.
“I want to hear from Arsenal fans this morning because I think they should at least tip their hats to the Arsenal hierarchy. For once you’ve got to salute the business that has been done here.
“Especially when you take into account that Arsenal were up against Napoli in the talks, they were up against Everton, they were definitely up against Manchester United, they were up against Paris Saint-Germain, and there were other Serie A and La Liga suitors over this boy’s signature.
“And they’ve nailed it, they’ve got him, £72m.
“It is a club-record fee and I would not be surprised if Arsenal fans want to show up in their numbers this morning.
“Get in touch with us and say ‘fair play, fair play’.
“Pepe, [Pierre-Emerick] Aubameyang and [Alexandre] Lacazette – what a front three.
“If you can’t get excited about that, when you see what this guy Pepe can do for the Ivory Coast and Lille, then you will never get excited in football.”
Arsenal are also keen on signing Celtic left-back Kieran Tierney and have seen two bids turned for the Scotland international.
And Glaswegian White is confident Arsenal will get that deal over the line as well.
“Will they get Kieran Tierney over the line? I think that they will, I honestly think that they will,” White continued.
“They will do business before next week and I’m sure that will happen as well.”