The 25-year-old – who starred for his nation in their opening game against Brazil – is valued at £8m, and has only been at his current club for 18 months after breaking through at Dortmund.
But rumours suggest that the Bundesliga side could be willing to cash in for a respectable fee, which has alerted Everton.
The Toffees are believed to have been paying close attention to Perisic in recent times, with scouts said to have assessed him in a World Cup warm-up clash with Australia.
Roberto Martinez is known to be in the market for additions in the coming months as he plots to replace loan stars such as Gerard Deulofeu and Romelu Lukaku and build a squad able to cope with the demands of Europa League football.
Perisic is seen as a potentially wise buy as he can operate on either flank or in a central role off of a main striker.
Everton have also been linked with Barcelona’s Cristian Tello.