However, the Gunners are less likely to sign Monaco midfielder Thomas Lemar, 21, having also had a bid turned down.
Meanwhile, Arsenal have not yet received any bids for 28-year-old Chilean striker Alexis Sanchez.
Sanchez has only a year left on his contract and may be allowed to leave for the right price.
However, letting Sanchez leave would depend on various factors, such as what reinforcements Arsenal have in place and where the interest was from, as they would be reluctant to sell him to another English club.
The North London side do still hope Sanchez, their top scorer last season, will sign a new deal.
Arsenal have had a bid rejected for 26-year-old French striker Alexandre Lacazette from Lyon, but negotiations are still ongoing.