The Gunners are scheduled to play friendlies against Sydney FC and the Western Sydney Wanderers this month, but Perez’s absence from the tour is a clear indication that his future lies elsewhere.
The 28-year-old is keen on a return to La Liga after a difficult first season in the Premier League, and will remain in England and train at London Colney while he considers offers from Spain.
It is understood that Perez’s former club Deportivo La Coruna want to re-sign the forward, but Arsenal will not sell the player for less than the £17million fee they paid for him last summer.
Deportivo manager Pepe Mel says the striker would be welcome back to Deportivo, but the asking price could prove a stumbling block: “Everyone understands that Depor wants Lucas.
“I know Arsenal well, they do not give away anything, especially if they have paid more before.
“I told the president to work hard on plan B, because it will probably be the most feasible. But of course we would be waiting with open arms for Lucas because it would make us a team with many more options.”
Perez still dreams of representing Spain at next year’s World Cup, and feels only regular football will give him a chance of featuring in Russia.
However, Alexandre Lacazette’s record £52million arrival from Lyon will move the Spaniard further down the pecking order at the Emirates, and also casts a doubt on the future of Olivier Giroud.
Everton, Marseille and Lyon remain in the hunt for the Frenchman, but it is thought Giroud is ready to stay and fight for his place in the team.