The Gers prevented the Hoops from picking up a historic 10th straight Scottish Premiership crown last term, finishing the campaign 25 points clear of their bitter rivals.
Since then, Celtic have welcomed Australian manager Ange Postecoglou into the dugout, and with both sides having already dropped points in the league this season, Smith is anticipating a much tighter affair at the top.
Speaking to GlasgowWorld, the ex-Ibrox midfielder said: “If you’d asked me that [who would win the league] this time last year, I would have said Celtic - Rangers can challenge - but Celtic will win the league.
“This year I think it’s probably the same - I think Rangers, but Celtic all of a sudden are looking as if they’re beginning to improve and they’re looking as if they can put in a challenge.
“Their [Celtic’s] form of late, over the past couple of games, has been quite impressive. They’re a very good attacking team, and if they can sort out their defence, they’re going to be quite strong.
“It’s very hard to say [who will lift the title]. I would say at the moment that Rangers have a better squad of players all-round, and I think they will win the league, but you never know in football.
“Last season none of us could have predicted how comfortably Rangers would win the Premiership.”
Smith also discussed the financial implications of Rangers failing to qualify for the group stages of the Champions League.