Arsenal look keen to sign 21-year-old France international Thomas Lemar from French club AS Monaco.
The young France international had been instrumental in Monaco's campaign last season where they won the Ligue 1 title after 17 years. The season also saw them reach the semi-finals of the Uefa Champions League.
But even though the London club saw their first two bids rejected, it appears they remain keen on doing a deal with the Ligue 1 champions holding out for Â£50million.
As reported by The Express UK, Sky Sports' Aidan Magee had this to say: "We are told discussions are ongoing over the future of this man - attacking midfielder Thomas Lemar.
"Arsenal have already had two bids of Â£30m and Â£40m rejected by Monaco. The Ligue 1 side are thought to be holding out for Â£50m.
"Head coach Leonardo Jardim, meanwhile, has told reporters that he can't guarantee they'll keep all their important players", Magee said.
This season could see the London club spend more than 100m for the first time in their history, something that has never happened in the clubs history.
Earlier this summer, Arsenal successfully acquired the services of another France international, striker Alexander Lacazette for a record-breaking â¬60m from Olympic Lyon. Their biggest signing in history, eclipsing Germany international Mesut Ozil's arrival (2013) from Real Madrid for Â£42.5m
Arsenal would not be participating in the Uefa Champions League for the first time in 20 years, having finished outside the top four last. The last time they failed to do so was in 1997.
But not having to play in the Champions League might be a good thing, as the boss says he wants to make the league his priority this season.Wenger also aims to give young players a break in the Europa League, according to The Guardian.
"For us, it is a good opportunity to focus completely on the Premier League"
"In the Europa League, if we can afford sometimes to rest some players, we will do it. But we have to adapt to the level of the competition and see, first, what kind of group we play in,"Wenger said.
Arsenal play Chelsea in the FA Community Shield at Wembley on Sunday to kick off the new season.