The 24-year-old, currently playing for PSV Eindhoven, travelled to England to thrash out contract details on Sunday, and was given clearance to enter the country.
"Alex was due to arrive into England yesterday to discuss personal terms," Chelsea announced.
"Chelsea Football Club are in the process of applying for a work permit for the player in line with normal football and employment procedure.
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"At airport immigration there was a request to clarify Alex's current status. All of the paperwork for his entry was in order.
"After an initial delay, he was cleared to enter the country. He chose voluntarily to fly back but will return when necessary."
One possible obstacle to the signing could be the requirement of all non-EU players to have played in 75 percent of their country's matches during the last two years. Alex has only played in only eight of Brazil's last 14 games, or 57 percent. A hearing is set to determine whether he is granted the required permit.
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