"I'm going to take my time. It will be two to four weeks before an appointment is made. I want to make sure we get the right calibre person."
Chief operating oficer Paul Douglas added: "We are an attractive proposition.
"We're top of the league and have a chairman with a track record of supporting his manager and being very ambitious.
"We do not expect applications to come from people currently employed and through the whole process we will keep our options open. "There are still CV arriving and interesting ones at that."
Stewart added:"I'm looking for someone with a good track record who can work well with the players and the directors and take us onto the next stage.
"It's true, I have talked a lot in the past about the importance of having an attractive, exciting product on the pitch. I want someone who will come and promote exciting, head-turning football in the style Kevin Keegan used to pursue, without the goals going in at the other end!
"We're in the entertainment business and we need to lift the expectations of the people of Rotherham. We need exciting football because people don't come to see the manager and the directors. It's about what goes on on the pitch. "I like enthusiasm and vitality. I like people with passion and drive. I want to see people jumping up and down when a goal goes in like I do. I've never scored as many goals as I have this season!
"We want someone with the experience and skills but I don't want to typecast him. It could be someone who is young or 50 odd years old.
"The townsfolk have supported this club in the past but finances have dragged it down. That problem has gone now," he said.
"We have a chance to bring in our own people. I've more knowledge than I had this time last year but I will still be advised by people in football. "We are having good imput from managers all over the country.
"We are already attracting the right calibre people because of our position in the league and financial strength. We've a lot to offer."