The Gunners had looked certain to sign the centre-back last week.
But their arch rivals Tottenham threw a spanner in the works and tabled a higher offer worth around £27m.
However, according to Caiazzo, Arsenal are progressing with the deal.
“Everything is on the right track with Arsenal,” he explained. “William will do next season with us.”
READ MORE: Man Utd agree £80m Harry Maguire transfer
“Arsenal are set to sign William Saliba”
Saliba is not deemed ready for Premier League football by Unai Emery and will be sent back to Saint-Etienne on loan.
Gunners hero Perry Groves isn’t impressed with the arrangement, though.
“They’re in for William Saliba from Saint-Etienne, the 18-year-old,” Groves said on talkSPORT.
“It’s £26m, they’re going to loan him back for a season.
“Arsenal aren’t in that position at the moment where you can loan players back. We need players to play now.
“If you were Liverpool or Man City, you’re in that privileged position then to think about next season or the season after. We need these players now.
“I know it’s going to be stage payments, but I want all of the budget going on players now that are going to come and make an impact in out first team.”
Arsenal couldn’t manage a top-four finish last season.
They also lost the Europa League final to Chelsea in Baku.
Groves fears another campaign of relative mediocrity beckons for his former club.
“I know we’re battling to be best of the rest again. Realistically, that’s fourth,” he added.
“Manchester United are in a bit of turmoil – [manager Ole Gunnar] Solskjaer is not going to be good enough.
“Chelsea are in a little bit of turmoil; they can’t sign any players, they’ve got Frank Lampard [as manager], and they’ve got young players coming in.
“So fourth place is really going to be competitive and I want us to be in a position to be able to compete.
“I know it shows how far we’ve dropped, competing for fourth place – but we’ve got to be realistic.
“And if they sign these younger players, hungry and with the right attitude, then as an Arsenal fan at the end of the transfer window I’ll think, ‘OK, we’re looking to go forward’.”