McCoist has refused to get drawn into the power struggle for control of the stricken Glasgow club.
The Gers manager has preferred to concentrate solely on football matters and has steered his team to the top of SPFL League One.
But he admitted the threat by the Rangers Supporters' Assembly, Association and Trust on Friday to "disengage with the club" was worrying. Light Blues fans refusing to buy season tickets or club merchandise would clearly impact upon his side on the park.
And McCoist has reiterated his hope that supporters continue to back his players during the off-field unrest.
He said: "I asked the fans, who have been fantastic, to give us their continued support. We feel they are doing that.
"They are well within their rights to say what they have got to say and feel how they feel. If it [a boycott] arises, it will possibly be a concern, but we would have to cross that bridge when we came to it."
McCoist, meanwhile, has expressed hope that pressure on his team intensifies in the weeks ahead - as a result of their winning run continuing.
McCoist has stated repeatedly that he does not believe Rangers can win all 36 of their games in the third tier this term, but he has stressed they will be doing their utmost to keep their hot streak going in the remainder of the season.
He said: "There is always the potential for slip-ups. We will obviously do our best to make sure that complacency doesn't creep in.
"I would be very disappointed if we were to get complacent. We will guard very closely against any complacency.
"A lot has been said about where we are. But in terms of winning games they have put together a record they should quite rightly be proud of."
"We will do everything that we can to keep it going."
Meanwhile, McCoist will meet with Rangers finance director Brian Stockbridge this week to finalise his much-publicised pay cut.
McCoist revealed at the weekend that the changeover of chief executive at the Ibrox club had prevented him from signing a new contract.