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Derek McInnes' side could move top of the Scottish Premiership this evening with a win over Dundee at Dens Park.
Rangers then have a Premier Sports Cup semi-final in store against Aberdeen later this month.
Hutton, who recorded over 100 appearances for the Ibrox club, thinks their lack of European commitments can be of benefit.
"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," Hutton told FootballPredictions.com.
"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.
"They've got their foot in the semi-final. Again, the fans will feel that they should go on and win that. It's not going to be easy, but there's an opportunity there.
"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."