The Gunners were widely expected to snare the centre-back last week.
But Tottenham derailed the deal and tabled a higher offer worth around £27m.
Nevertheless, his move to the red half of north London is back on track.
According to The Sun, the 18-year-old will complete his medical on Tuesday.
“Unai Emery looks set to sign William Saliba”
Once he’s signed on the dotted line, Saliba will then return to France on loan.
Arsenal have made just one acquisition in the last few weeks.
Gabriel Martinelli, 18, was bought from Brazilian side Ituano.
Once the ink is dry on Saliba’s contract, Emery will focus his efforts on other players.
The Premier League heavyweights have a long-running interest in Celtic star Kieran Tierney.
The £25m-rated full-back has impressed at the Scottish champions and is being watched by a host of clubs.
The Gunners are also working on a loan move for Real Madrid midfielder Dani Ceballos.
Wilfried Zaha is still firmly on the agenda, but Crystal Palace value their influential forward at around £80m.
Emery has made it clear he won’t spend for the sake of it.
“Really I am with patience because we want to choose the best solution,” he said after Arsenal’s 3-0 pre-season win over Fiorentina.
“Some players are very expensive and we are waiting for this possibility.
“We don’t want now to go to the second line of players. We are waiting. We have very good players.
“We have very good young players. We are aware also that we need to improve some players in this squad.
“I want to sign one, two, three or four players only if we can be sure they are coming to improve our team.”
Zaha’s brother, Judicael, wants Palace and Arsenal to strike a deal.
He told Sky Sports News: “Wilfried will always hold Crystal Palace and their fans in the highest regard and all the support they’ve given means the world to him.
“It’s my brother’s dream though to play for Arsenal.
“Given all Wilfried has given to Palace to help them remain a Premier League club, I hope Palace will be able to see their way to agreeing a deal with Arsenal that allows Wilfried to realise his dream of playing European football for the club he’s supported since childhood.”