The 37-year-old says he has a good feeling about the squad as the new signings settled in to pre-season training this week.
Speaking to RangersTV he said: “I think we had a decent end to last season apart from obviously the last game but the way the team is shaping up I think the fans have got a lot to look forward to.
“I don’t want to say what my aim is but it is obvious and it was the same goal last year but we didn’t actually do it so hopefully we can change things and be more consistent, I think that was our biggest problem last season.
“I do have a good feeling about this squad. I think everyone is champing at the bit to win something for themselves, their families and the fans. It has been a long time so hopefully we can make it right this year.”
With the Europa League qualifying rounds being drawn this week, McGregor is also hoping the squad can go on a run in the competition.
He added:
McGregor has been joined at preseason training by Jak Alnwick, Wes Foderingham, Andy Firth and Robby McCrorie and is enjoying the chance to work with the group of goalkeepers.
The squad will spend next week at a training camp in Portugal as they prepare for the first Europa League game in just four weeks.
“It is always competitive so it is a good thing for me, it is enjoyable,” he said.
“I dreaded pre-season, even when I was 16. Every year I have nightmares about it when I’m on holiday, but it has to be done and I think it benefited me last year.”