Former Chelsea and Arsenal winger Willian is keen to return to England and has been offered to a Premier League club.
Willian, 36, left Olympiacos last month just five months after joining the Greek side.
The Brazilian winger is hopeful of continuing his playing career and his representatives have approached Everton to discuss a possible move to Goodison Park.
According to The Times, Everton are now weighing up a deal for Willian, though the veteran has also been offered to other clubs.
Everton have struggled badly in the final third this season, scoring just 15 goals in 20 Premier League games.
The Toffees found the back of the net just once in Sean Dyche’s final five games in charge, the experienced manager sacked last week with Everton in a precarious position in the Premier League.
Everton failed to score yet again in David Moyes’ first game back in charge of the club in a 1-0 defeat to Aston Villa, and the ex-West Ham boss is keen to bolster his attacking options in the January transfer window.
Willian could be an attractive proposal for Everton despite his dismal spell in Greece as he impressed for Premier League side Fulham just last season.
The former Brazil star spent two years at Craven Cottage after playing for London rivals Chelsea and Arsenal earlier in his career.
Willian thrived at Stamford Bridge, making over 300 appearances for the Blues and helping the club win two Premier League titles, the FA Cup and Europa League.
For a period Willian was one of the most consistent wingers in the Premier League but he flopped at Arsenal, scoring just once in 37 games before leaving after one season.
‘I wasn’t happy [at Arsenal], I wasn’t happy,’ Willian said on Manchester United and England legend Rio Ferdinand’s YouTube channel when looking back at his time at the Emirates Stadium.
‘That’s why I didn’t perform. I don’t want to go into the details. When I arrived there I was happy, from the beginning I was motivated, I wanted to do well – new club, new mates, new project.
‘But after three months, I said to my agent: “Please, I want to go”. I don’t want to speak bad about the club, because it is a big club. Arsenal has a big history.
‘In football, big players played there before as well. But it didn’t work, it didn’t work. It was, of course, the most difficult time of my career.
‘It was big money that I gave up. But sometimes money is not the most important thing in life. I think you need to be happy, get pleasure every day waking up in the morning to go to train. I wasn’t having that.
‘So I said to myself, with my family, I cannot stay here, I am not happy here. I have to leave, find a way out, leave the club, because if I stay I am going to stay the same.
‘For me, it’s unfair to stay in a place that you don’t want to stay just because of the money. For me, it was that.’
Moyes will look to securehis first points since returning to Everton on Saturday when struggling Tottenham visit Goodison Park.
Everton are currently just 16th in the Premier League table – one point above the relegation zone – with 17 points from 20 games.
Discussing the need for January reinforcements, Moyes said after the Aston Villa defeat: ‘I can definitely see we are lacking a level of quality that will give us opportunities or make us more goals or score more goals.
‘We’d like to address that if we can.’
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