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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Since Guus Hiddink arrived at the helm, Chelsea have improved considerably after a tricky start to the campaign.
Newcastle United are staring down the barrel of relegation to the Championship for the second time in the past eight years.