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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Chelsea have struggled to build momentum in the opening stages of the campaign and are currently looking over their shoulders at the relegation zone.
Who of Europe’s top strikers will move to England this summer?