Carrasco has spent just over a year at Chinese Super League outfit Dalian Yifang.
But the Gunners are known to be keen and are believed to have been close on finalising a deal for the Belgian for days.
And now the winger, who formerly played for Monaco and Atletico Madrid, has admitted he wants to be back in Europe.
“The whole world knows that I want to return to Europe,” he said.
“Now, it depends on the president and I hope he finds a solution.”
Asked about Arsenal he added: “I can’t speak about the club.
“Now I am not the one who chooses, but my president.
“He decides if he lets me go or not, but I hope I can come back.”
Carrasco scored for Atletico in the 2016 Champions League final against Real Madrid in a losing effort.
He would be Arsenal’s first signing of the summer with Unai Emery expected to have a busy window.
The Spaniard may be restricted financially though recently admitted he needs to spend if he wants to improve on Arsenal’s fifth-placed Premier League finish.
He said: ”I think we can improve first, by spending money to achieve players.
“In the past the club have done great work in watching players, finding and signing young players and developing our players in the academy.
“I have big respect for our work, for our players in the academy.
“I want to develop the players here—giving them progress to achieve something at a big club like we are.
“We can also achieve [buy] some players who are in other teams, who can come here and give us this performance—like [Virgil] Van Dijk with Liverpool.”