Sturrock said: "Peter Brezovan is on a two-day trial with Everton and it is a tremendous opportunity for him.
"Everton have had good reports about him and offered him a short trial."
Brezovan joined Swindon on a season long loan from Czech Club FC Brno, and they signed for Swindon this summer, but hasn't played any league games for Swindon for nearly a year. He made a great start to last season but broke his arm last October, and Phil Smith took over in goal. As Smith has done well since he has kept his place, and has kept Brezovan out of the goal.