The 32-year-old has been handed the reins following David Hopkin’s resignation earlier this week.
City have received more than 60 applications and the board plan to spend the weekend assessing their options.
“It has never crossed my mind,” said Drury, assistant to Hopkin and Michael Collins this season, when asked if he was interested in taking charge on a permanent basis.
“I spoke to Julian (Rhodes, chief executive) and Stefan (Rupp, owner) and made it clear to them I am a coach.
“I have a genuine passion to help the football club. I am an employee of the football club. I have an affiliation here. I will do it for now and to the best of my ability.
“I have been here three or four years and am very passionate about this club. We have to improve.
“This club has to gain its identity back. It has been a difficult 18 months. The powers-that-be are working hard behind the scenes to make the decision as to who comes in that can take this club forward.
“I will do all in my power to ensure whoever comes into the building will do so on the back of a win.”
Drury has made one big decision already in handing the captaincy from Anthony O’Connor to Paul Caddis.
The caretaker manager added: “Paul has been one of the most consistent performers in the group since he joined the club. He is well respected by the players and staff.
“I just felt that Anthony O’Connor has played a hell of a lot of football this season.
“We have kept clean sheets at times and Anthony has played an integral part of that. But there has been an inconsistency within the group and we are in the top five in the league for goals conceded.
“There has been an inconsistency of performance and Anthony has taken a lot of that burden upon himself this season.
“I just wanted to take that pressure off him and give it to Paul, who I know can handle those expectations having had the career he has had.
“But whoever has that armband on is not that big a deal. I need 11 captains out there on Saturday.”