Ally McCoist is not allowed to strengthen his Gers squad due to a 12-month signing embargo imposed by the SFA for the non-payment of taxes during the Craig Whyte era.
But midfielder Hutton believes there is already competition for places at Ibrox – and is sure their form will not dip in the Irn-Bru Third Division or William Hill Scottish Cup.
He said: "We haven't even thought about the window. We have just been concentrating on the football side of things and winning every game that we have played.
"It is a bit strange that nobody will be coming into Rangers this month. You hear a lot about other teams going out and signing players at this time.
"When a player who plays in your position comes into a club there is obviously a fear that he will take your place. Bringing in new faces definitely helps to keep you on your toes.
"But we feel as if we have got a healthy squad here just now. There is competition for places.
"Even though we can't sign players, there is still a worry there that somebody will come in and take your place. There are a lot of great players here and you are always wary.
"We all know we have to play well at the moment to keep our place in the first team."
Hutton, too, is confident that Rangers gaffer McCoist will be able to keep his current pool of players together during the January transfer window.
He said: "There is a danger other teams could try to sign some of our players. But Rangers is a massive club and I am sure that all of the boys who are here see themselves playing here for as long as they can.
"All the players here know what they have at Rangers. It is a great club and we are supported by a lot of fans. If someone else did perhaps come in for one of our players I know they would think long and hard before giving it up.
"I think the best thing would be staying. I am sure all the other boys are the same."
Hutton, who was frustrated at being left out of the side at the start of the season, knows he has to continue to perform in every game now that Ian Black has returned to full fitness.
The pair formed the central midfield partnership in the narrow 1-0 win over Queen's Park at Hampden on Saturday.
However, Lewis Macleod was absent and when he returns to the fray McCoist will have a selection headache.
Hutton said: "I am getting a mini-run in the side at the moment. I scored my first goal for the club the other week against Elgin as well.
"Wee Blacky is back fit now and played in the game against Queen's Park at Hampden on Saturday.
"I know I need to perform in every single game in order to keep him out of the team.
"Hopefully, I can be involved in every single game."