The 22-year-old has made 13 appearances for Everton this season.
Everton manager Ronald Koeman last week said the player would be allowed to leave to "get game time".
The Spaniard joined Everton on loan from Barcelona for the 2013-14 season, making the transfer permanent in 2015 for £4.3m.
Milan originally announced the move via their official Twitter account on Friday, but it was quickly deleted.
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The 18-hour spiritual fasts are not easy and for some the month can be a difficult challenge, especially for people with eating disorders.
Amina Clayton, who is 19 and lives in Birmingham, is recovering from an eating disorder after having symptoms of both anorexia and bulimia.
She was diagnosed at the age of 16 when she was "hardly eating anything and became very obsessed with exercise".
Now Ramadan can bring back painful memories.
"The hardest thing about Ramadan is that it's all centred around food," she says.
"For me, the fast in the day is easier.
"It's at night that it's more difficult when families gather after 18 hours of fasting to break the fast," she adds.
Amina explains that the problem lay in the fact that she was eating at night and then very early the next morning.
"In a space of five or six hours, that's all your intake until your next fast begins so it feels like a binge," she says.
"Of course it's not a binge as your body needs that energy to fast the next day."
She says it is important that people with the condition realise that Muslims do not have to fast if they are unwell.
"Last year I didn't fast at all, and that was a difficult decision to come to because my faith is important to me," she recalls.
"To realise fasting might be detrimental to my recovery was the right decision though."
This year she has decided to fast on some days.
Amina says there had been one particularly difficult evening with her family, when they had all started eating after breaking their fast.
"I was having a good time and hadn't really been paying any attention to what I'd been eating," she explains.
"And then when I realised, I felt a lot of the feelings I've felt surrounding food, and the guilt and shame of not being in control.
"I had to fight quite hard the urge to make myself sick," she points out.
Amina says confiding in her mum, as well as speaking to Muslim doctors about fasting during Ramadan, has helped her.
Usman Mahmood, an imam from Birmingham Central Mosque, outlines that advice.
"Any sort of worship where health becomes an issue, that worship has to stop," he says.
"Instead of fasting, people can pay Fidyah where they pay over the month for a poor person to eat."
Source: Beat
The eating disorder charity Beat says people have reported difficulties to them during Ramadan and other religious occasions.
"Food is central to a lot of religious festivals. So Christmas is another time where someone with an eating disorder may experience difficulty," says Lorna Garner from Beat.
"People with eating disorders fall into the category of people that are unwell so are exempt from fasting, [so] it sometimes helps people to seek religious guidance.
"Family members too could encourage a sufferer to look for other ways of observing Ramadan, perhaps giving to charity," Lorna adds.
Maha Khan, who was diagnosed with anorexia, has started the Islam and Eating Disorders blog to raise awareness in the Muslim community.
She told the BBC that she had been contacted by people with concerns during Ramadan.
"Fasting is a vital part of eating disorders, and there is added social pressure because people come together to eat in the evenings," she says.
"There is a lack of awareness in some Muslim families.
"I try to bring in the Koran to emphasise that when you need the medical treatment, you have to go to your doctor," she adds.
Amina reinforces that point. "Religion shouldn't stand in the way of recovery, it should aid it," she says.
"It took me a while to realise that not fasting last year doesn't make me a bad person, it makes me a good one. I made a choice to look after my body and mind."
Everton winger Gerard Deulofeu has joined Italian side AC Milan on loan until the end of the season.
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It is coming to the end of Ramadan, when Muslims fast between dawn and sunset for a month.