Aberdeen finished second in the recently concluded 2014-15 season with 75 points from 38 matches.
Although the Bhoys clinched the championship with relative ease in the end, Derek McInness’s side did give them a scare in the opening months of the campaign.
Collins has admitted that the Dons will once again push Celtic hard for the Premiership title in the 2015-16 campaign.
“There is no doubt the main challenge will come from Aberdeen,” the 47-year-old told The Scottish Sun. "They gave us a terrific challenge last year and pushed us all the way.
"They have added a few players so have strengthened their squad and Aberdeen will be our main rivals. I expect Hearts to be a good challenge as well.”
The Edinburgh-based outfit won the Scottish Championship ahead of Rangers and Hibernian in the 2014-15 campaign.
"We can try and outdo them and try and win the league and it's a fantastic battle and opportunity for everyone else," the 37-year-old former Rangers goalkeeper Alexander told BBC Sport.
Collins has also suggested that Celtic may not be able to sign Ikechi Anya or Steven Fletcher in the summer transfer window.
Scotland international winger Anya is on the books of newly-promoted Premier League outfit Watford at the moment, while striker Fletcher currently plays for Sunderland.
“They are two players I like,” Collins told The Scottish Sun. “But they are Premier League players and everyone knows what the salaries are like in the Premier League.
"That said, we would maybe like another couple of players to come in before the start of the season.”