A big 1-0 win over Brentford at home has taken Everton out of the relegation zone and up to 15th in the Premier League table.
Barring a home defeat against Aston Villa, Everton have won the other three Premier League games they played at Goodison Park since Dyche took charge of the club last month.
Gray stressed that the Everton manager has added some grit and steel to the Everton side.
He has seen them fight in the games they won at home in recent weeks and feels they now look like a team who are going to survive in the Premier League this season.
Gray said on talkSPORT’s GameDay: “I have seen them play the last three games at home barring the Aston Villa defeat, where they have won all three games.
“I have seen some fight where Sean Dyche has brought something different to this Everton side.
“At the moment yes [I can see them staying up].”
Everton will next be in action next weekend when they take an away trip to Chelsea ahead of the international break.