Tuesday's Daily Record made the claims, which come in the wake of the departures of head scout Neil Murray and physiotherapist Pip Yeates and the sacking of striker Francisco Sandaza.
McCoist and McDowall worked under Walter Smith during his second successful spell as boss at the club until the former Rangers striker took over the hot seat in 2011 with Durrant promoted into his backroom team.
McCoist was keen to make that clear when asked about the issue at a press conference to publicise Wednesday night's friendly against Linfield at Ibrox.
He said: "I can confirm to you right now that I have not entered into any discussions at all with Charles regarding Kenny or Ian.
"On that subject, all I would say is that in the last five years, Kenny, Ian and myself, with Walter, have won three SPL titles, some cups, got to a European final, had a season under Craig Whyte and then we won a title this year.
"That's all I go to say on that matter, I'm not going to take it any further."
Asked about the extent of his involvement in decisions at Ibrox, McCoist replied: "I am involved. I obviously don't have the final say but I like to think my input, a, is valuable; and b, is taken on board. That's an important message to get out."
After Rangers had beaten Queen's Park on Sunday in their first match since clinching the Irn-Bru Third Division title, McCoist responded to Green's assertion that it was the worst team ever to wear the Light Blue by saying: "In my opinion, it's not the worst Rangers team.
"I'm not sure how many titles Charles has won in his career but I've been very fortunate to win 14 at our football club, including as assistant manager."
- Sports & Recreation
- Walter Smith