Physio Pip Yeates, chief scout Neil Murray and striker Fran Sandaza have all left Ibrox in the last fortnight and it has been claimed that chief executive Charles Green urged McCoist to axe Durrant and McDowall as part of his restructuring plans.
But McCoist insists he has not discussed the pair's future with Green and pointed to the recent success the club have enjoyed with the coaching set-up.
"I have not entered any discussions at all with Charles regarding Kenny or Ian, my coaching staff," he said.
"On that subject, all I would say is, the last five years I think it is, Kenny, myself and obviously with Walter (Smith) have won three SPLs, cups, got to a European final. Then we had a season under Craig Whyte and then we won a title again this year.
"So that's all I've got to say on that matter. I'm not going to take it any further."
McCoist admitted he is getting frustrated with such speculation as he feels it takes the attention away from his team, who secured the Division Three title last month.
"It's frustrating in the respect I'm getting a little bit annoyed at our team not getting spoken about and congratulated," he said.