The Dons host the Premiership champions on Friday night before Scotland's top two clubs meet again in the Scottish Cup final on 27 May.
"We want to show we can beat Celtic, because we know we've got the players that can," McLean, 25, said.
"I think we are the best team to stop the unbeaten run - and stop the treble."
Aberdeen were brushed aside by Celtic in November's League Cup final and have lost all three of the sides' previous league encounters this season.
"There is a lot at stake because we want to have momentum going into the final," former St Mirren midfielder McLean said. "That's what it's all about now.
"We've not taken anything from Celtic this season and we're disappointed from that.
"We have done well, but ultimately we've not picked any points up, which is disappointing, no matter how well you do.
"Picking up points against Celtic would be a massive boost for us and it would give us confidence going into the final.
"They've been outstanding, the best team in the league by far this year, so we know it's going to be a tough task, but we've definitely got the ability in the squad to hurt Celtic."
McLean has scored five goals this season, helping Derek McInnes's side all but secure second spot in the top flight.
With three league games remaining, the nine-point advantage and significantly superior goal difference Aberdeen have over third-placed Rangers should ensure they finish as runners-up.
"At the start of the season, a lot of people didn't think it would be the case, but we were always confident with the squad and ability we had," added McLean, who has one Scotland cap.
"It's been a real togetherness this season from everybody; the relationship between the fans and players and staff has been excellent.
"We've always been confident that we can be the nearest challengers to Celtic and we've proved that again, and proved most people wrong, I would say.
"And it's just up to us to keep pushing ourselves on and keep being in that position, to keep channelling ourselves to get better."

Ling Jihua pleaded guilty and "decided not to appeal", state media reported.
Ling was in effect chief-of-staff to Mr Hu, but was demoted in 2012 amid a high profile anti-corruption campaign.
His downfall came after reports of an alleged cover-up over his son, who died alongside two semi-clad women while driving his Ferrari in Beijing in 2012.
There was also speculation that Ling's demotion may have been the result of political manoeuvring ahead of a leadership change that year.
The court in the northern city of Tianjin held a closed-door hearing on 7 June, Xinhua reported.
Ling was convicted of taking $11.57m (Â£8.71m) in bribes and to have used his influence to secure property deals and promotions for his associates, among other favours, the state news agency said.
Until the scandal involving his son, Ling had been tipped for promotion to the party's Politburo.
Instead, he was moved from head of the Central Committee's General Office - in effect chief of staff to China's leader - and appointed to the less influential post of head of the United Front Work Department.
The identity of those inside the Ferrari was never revealed and censors blocked online comments mentioning the crash. Ling was accused of trying to cover up the scandal.
The authorities announced an investigation into him in late 2014, and he was expelled from the Communist Party and arrested in July 2015.
President Xi Jinping has overseen a campaign against corruption since coming to power in late 2012 and many high-profile political figures have been jailed.
Critics say President Xi's campaign is as much about eliminating political rivals as it is about tackling corruption.
Kenny McLean insists Aberdeen can end Celtic's unbeaten domestic run - and derail their bid for a treble.
[NEXT_CONCEPT]
An ex-aide to retired Chinese president Hu Jintao has been jailed for life for corruption, illegally obtaining state secrets and abuse of power.