The Millers are set to step up their search for Steve Evans’ successor during the international break after being inundated with applications for the post.
A host of names have been linked with chairman Tony Stewart admitting that interest has also come in from abroad.
United are not in action until October 17 and the hope is that an appointment will be in place before the trip to Brentford.
Collins, stand-in captain in last Friday night’s defeat to Burnley, said: “The priority last season was to stay in the league. But our task and ambition this time has to be bigger than that.
“We got ourselves out of the bottom three and with a win against Burnley we could have been 13th going into the international break. We have to take positives, we had some good performances.
“There is a good atmosphere around the place and, hopefully, that can continue after the break.”
United headed into the break sitting outside the bottom three on goals scored.
On the search for a new manager, Collins added: “The boys have looked at the odds over the last few days and who has been linked with the job. But, I won’t spend the break watching Sky Sports News every day.
“We will be in for training and trying to continue what we have done over the last few weeks, which is put in good performances.”
Evans’s abrupt departure a week ago took many by surprise, as Collins admitted. “My reaction to what happened was more shock than anything. At the timing of it, really.
“Earlier in the season, when we had not won in five or six games, if it had come at that time then you might have thought, ‘Fair enough’.
“But we got back-to-back wins, looked to have turned the corner but then it came out of the blue. From our point of view, our job is to get out on the training pitch.
“Eric Black (caretaker manager) took us in the week and against Burnley, and things have been good.
“There has been a good atmosphere around the place and I thought that showed in the majority of our performance (on Friday night).
“Nine times out of 10 when a manager changes, you are in a bad patch but that has not been the case here.”