Aberdeen sit between Glasgow rivals Celtic and Aberdeen in the table.
Celtic's loss to Hearts has given hope to the rest of the Scottish Premiership, with the champions' air of invincibility now gone.
Brendan Rodgers' side were beaten 4-0 by Hearts, and the chasing pack now have an opportunity to put them under pressure.
Aberdeen chairman Stewart Milne has though sought to downplay his team's chances, and believes they alone cannot catch Celtic.
The Dons supremo believes if enough teams can beat Celtic then Aberdeen may have a chance, and also added that he was pleased Rangers were beaten by St Johnstone.
He told BBC Sport: "It was fantastic to see the performance from Hearts on Sunday and also encouraging to see the likes of St Johnstone coming back [to beat Rangers].
"I think we've always said that if we're going to rein in Celtic, we need four or five other clubs that are part of that, keeping the pressure on them right through to the end of the season.
"I don't think any of us are going to get carried away and start speaking about title challenges. We just need to make sure that we take maximum points out of every game we play and then that'll take care of itself as we move through the season."
Aberdeen have closed the gap to four points on Celtic, and have now overtaken Rangers once again after the Gers had climbed above them.
The Dons have been consistent as the second best team in Scotland in recent seasons, and while they want to ideally go one better and topple Celtic, they also have to be wary of Rangers' renewed challenge knocking them back down to third.
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