The former Serbia Under-21 captain could then sign permanently next summer with the Goodison Park club having the option to purchase Stojkovic at the end of the agreement.
However, the 24-year-old will miss the first three weeks of the season playing for Serbia at the Olympics in Beijing.
Stojkovic’s agent Zoran Stojadinovic is finalising the paperwork and has confirmed Everton could purchase the player for around £2million.
Stojadinovic said: “The offer is a season-long loan, with an option to purchase the player definitively at the end of this period. The transfer fee is likely to be between 2.5 and 3 million euros.
“At this moment we’re just waiting for the visa to be able to travel.
“It was David Moyes who spoke to me. What Stojkovic wants is to play and if he goes to Everton he will fight hard with Howard to earn a starting place.”
Port Vale boss Neil Aspin is expected to choose from an unchanged squad for the home game against Exeter.