The 25-year-old was heavily linked with a return to European football from Chinese Super League side Dalian Yifang in January.
A move to Emirates Stadium was mooted at that stage, but no deal was done before the deadline.
It could be that another opportunity presents itself in the next window, with Carrasco ready to push for a switch after a little over 12 months in Asia.
He told The Sun: “There was interest from Arsenal and I had a lot of teams in January giving me the chance to go back to Europe, but here the president said it was difficult to go then.
“Maybe this summer it is possible. If it is a good thing and I want to go, maybe I can speak with the president.
“I try to do my best because I am a professional for my team and after we can think about a solution. If I have a lot of teams who want me but the president decides I have to stay, I cannot do anything.
“All that you want is to be close to your family, and to go back to Europe is a good solution.
“I’m OK here, the club is good with me, the players and fans also are nice with me.
“But you know, when you are far from your family, and I think I can do good things in the European game, I am thinking it’s a solution if I can go back.”
He added: “All the people know England is one of the best championships in the world, it’s a big competition.
“The players who play in the Premier League tell me it is a physical league, strong, but you also have a lot of space.
“Sometimes when you play in other countries you do not have a lot of space but in England it is open, the play is up and down the pitch.
“That would suit me. I think I can play in a lot of competitions in the world, I can attack and also I can defend.
“With the national team I play as a winger, but also I can play in behind. England would be a good competition for me. I think I would be OK.
“If I have the opportunity to go to England, why not?
“I don’t think if you play in China you lose your quality. You see Paulinho when he went to Barcelona. He stayed a lot of years in China, but he went to Barca and did well, and he played the national team and he did well.
“Now you see Axel Witsel with Dortmund, he stayed for one year in China and he also did very well with Dortmund.
“Why not me? I need to have something. I try to find a solution to be nearer my family?”