The Paraguayan has played abroad since 2001 and is a free agent this summer.
The Paraguayan, who had looked a competent defender during his time with Wigan Athletic and in the national team, struggled to get going at Everton from day one.
He arrived in 2013, following Martinez from Wigan, to provide some extra cover in the defensive department. But he struggled to find his best form and his woeful performance against Dynamo Kiev in the Europa League last term was a fitting demonstration of his Everton career, in what proved to be his final game for the club.
His contract expires at the end of this month and Everton have confirmed he will be leaving the club. Now it looks like he has a potential suitor, in his homeland.
It is reported by ABC in Paraguay that Alcaraz has already agreed personal terms with Club Libertad ahead of a potential return to his home nation.
He has not played in Paraguay since leaving Teniente Farina for Racing Club in Argentina back in 2001.
He has since gone on to have spells with Fiorentina, Beira-Mar, Club Brugge, Wigan and finally Everton in Europe.
Now it seems the time is right for the 32-year-old to go home.