The 32-year-old is currently at Galatasaray, where he scored five goals in 25 top-flight outings last term.
But now sources in Turkey have claimed that new Toffees boss Ronald Koeman wants to make his fellow countryman one of his first signings since being appointed at Goodison Park.
Koeman is said to have money to spend this summer, and former Real Madrid and Inter ace Sneijder has a release clause said to be as low as £5m – although his wages are likely to be high.
But the 53-year-old, who worked with the Holland international during his time at Ajax, believes he could fit into his new-look Everton side.
Some reports in Turkey have even suggested that the Merseyside club have already held early talks with Gala about a doing a deal this summer.