Boruc is without a club after leaving Fiorentina and the Daily Mail reports that he had a trial at Everton’s Finch Farm training ground on Sunday.
Everton boss David Moyes is looking to strengthen his squad in the free-agent market.
Boruc impressed during five seasons with Scottish side Celtic before joining Fiorentina in 2010.
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The reputation of the Premier League means it is the most popular and one of the most watched leagues in the world.
Five English clubs will compete in the last sixteen of the Champions League for the first time ever as Liverpool, Manchester United, Manchester City, Chelsea and Tottenham face some difficult away matches.