Zaragoza slipped into the relegation places after last weekend's 2-1 home loss to Athletic Bilbao and Gay was subsequently hired on a provisional basis to take over from the sacked Marcelino.
"I like to seize the initiative," Gay, who played for Real's B side in the late 1980s and later coached their C team, told Thursday's As newspaper.
"I know that it's possible the club is still negotiating with other coaches but I am full of enthusiasm and very excited about the job," he added. "Every coach dreams of being in charge of a team in the first division."
Cristiano Ronaldo is set to return to action for Real after he was suspended for last weekend's 3-2 win at Valencia.
The Portugal forward was criticised for the sending-off against Almeria that led to his suspension and returns as second-placed Real seek to take advantage of their game in hand over undefeated leaders Barcelona to cut the gap to two points.
Barca are in action at the Club World Cup in Abu Dhabi, where they take on Estudiantes in Saturday's final, and have 39 points from 15 matches. Real have 34 from 14, four ahead of Sevilla in third, who host eighth-placed Getafe on Saturday.
Real have also been boosted by the news that Ronaldo's Portugal team mate Pepe, who tore an anterior cruciate ligament in the Valencia game and will be out of action for around six months, was operated on successfully on Thursday.
WELL ADVANCED
Real's Brazilian playmaker Kaka, who has a groin problem, is set to miss the Zaragoza match but said on Wednesday he was looking forward to returning after his Christmas holiday.
"I am improving and my treatment is well advanced," he said at an event in Madrid. "I don't know when I'll be back on the pitch but I want to play when I get back from Brazil."
Sevilla striker Frederic Kanoute and defender Ivica Dragutinovic have been suffering from minor ailments and trained apart from the rest of the squad in the gym on Wednesday but should be avaliable for the Getafe clash.
