Arsenal are less optimistic of signing Thomas Lemar as they believe Monaco are unwilling to let another player leave the club this summer, according to reports.
Bernardo Silva joined City from Monaco earlier this summer, while teenage striker Kylian Mbappe has also been linked with a world-record move to Arsenal and Real Madrid.
Lemar scored nine goals in 34 Ligue 1 appearances to help Monaco win the domestic title last season. He has three years left on his contract at the French club.
Lemar's father said in an interview in April that his son planned on staying at Monaco for two more seasons.
"Today, Thomas is with the Ligue 1 leaders. There is no set plan for him," Edwige Lemar told Ouest France.
"We are of the belief that logically the plan is [getting more] playing time, which is what he has at Monaco.
"Sometimes there are financial parameters that do not fit into that, but I think that the aim is to do another year or two with Monaco. His ambition, his aim, is certainly to go a little further. In this situation, the player will have a say, but he is not always the only one to decide."
The Gunners have signed Alexandre Lacazette from Lyon for a club-record £46.5m ($60.7m) and left-back Sead Kolasinac on a free transfer from Schalke so far this summer.
Alexis Sanchez is reportedly keen to leave the Emirates Stadium in search of Champions League football, but Arsenal remain intent on holding on to him.
The 28-year-old forward, who has a year left on his contract, said over the weekend that he had made his wishes clear to Arsenal.
"The truth is that the decision doesn't depend on me," Sanchez was quoted as saying by the Guardian.
"I have made my decision, but now we wait for a response from Arsenal. It depends on them, I have to wait to know what they want."