Ally McCoist's side have been made second favourites for the William Hill Scottish Cup after being handed a quarter-final tie against Albion Rovers next month but are likely to have to overcome SPFL Premiership opposition if they are to achieve a remarkable silverware success.
Dundee United and Inverness Caley Thistle, who knocked Rangers out of the League Cup and Scottish Cup last year, are both still in the competition, as are St Johnstone and favourites Aberdeen.
McCulloch insists the Gers can prove the doubters wrong and claim a unique domestic trophy haul as they close in on the title and Ramsdens Cup final in April.
He said: "We're in a better place than we were last year. We have a bigger, better squad. We have more quality, we've had more clean sheets and scored more goals.
"Having a proper pre-season was massive. We've progressed and we need to keep that going.
"Training on Mondays and Tuesdays is really hard work and then we go into the technical side later in the week.
"Well, it would be three trophies and that, to me, is a treble. I'll be shouting about it, whatever we can win.
"People can talk and we've already been written off for the Scottish Cup - it's been said we're not in the top five to win it.
"That's just part and parcel of playing at Rangers. You take it on the chin and try to prove people wrong and that's what we're doing."
With Rangers romping ahead in the League One title race, their biggest challenge for the rest of the campaign will come in the Scottish Cup.
The champions are likely to be the only non-Premiership side left at the semi-final stage and skipper McCulloch would relish the chance to test themselves against Scotland's top teams.
He said: "Yes I think it'd be good this season. Last season we beat Motherwell and then we were beaten by Inverness and were beaten by Dundee United.
"But I think we're better equipped this season. That doesn't mean to say we'll go and wipe the floor with them. But it will be good to get a gauge, just to see where we are.
"I said the gap isn't as big in the Premiership as it is in the so-called lower divisions, and I still stand by that, but it got twisted a wee bit by a few people.
"What I was meaning was potentially the bottom six in the top flight to some of the teams in the lower leagues, I honestly don't see as big a gap as what people think.
"Maybe I didn't explain that well enough or whatever but I think the results are there and the standard is there for everyone to see."
While Rangers have been in superb form as they move closer to a potential treble, the picture remains muddy off the field in the midst of rumours about the club's financial position.
McCulloch was involved in the talks with chief executive Graham Wallace that resulted in the Ibrox squad rejecting proposals that would have seen them take a 15% pay cut but the Gers skipper insists it is business as usual at Ibrox.
He said: "Nothing changes. It's just about putting in hard work every day and staying positive and keeping all the boys together. It wasn't unsettling.
"We just focus on the football and try to win games. To be fair, the boys have done that and that is a credit to themselves.
Lee McCulloch was speaking as Rangers launched their quarter season tickets for the remainder of the League One campaign.
Tickets cost £85 for adults, £59 for concessions and £21 for juveniles and are available from the Rangers Ticket Centre, rangers.co.uk or 0871 702 1972.