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Under Derek McInnes, the team has a chance to move to the top of the Scottish Premiership with a victory over Dundee tonight.
Later this month, Rangers will face Aberdeen in the Premier Sports Cup semi-final.
Hutton, who played over 100 games for Rangers, suggests their lack of European engagements might work in their favour.
He told FootballPredictions.com: "Rangers will want multiple trophies, absolutely.
"I mean, it doesn't matter whether Rangers are in bad form or whatever, or whether the team at the start of the season doesn't look great.
"Fans go into the new season stating 'treble'. That's the bar.
"Celtic have won it for a number of years so that's the bar for the two Glasgow clubs.
"Unfortunately, Rangers have fallen short.
"I think this is probably a real sense now from this Rangers team that they can go and do something like that.
"It's easy to say it, it's harder to go and do it."
He continued: "Without European football, you've just got the domestic side to really focus on.
"That's what they'll be aiming for, this hasn't changed since I was there.
"So it's always going to be the same.
"The pressure's there, it's whether they can deal with it or not."