The Blaugrana were not favoured ahead of the season starting and in early December they remained languishing in the bottom half of the standings.
The Catalan giants endured a run of just two victories in eight league matches in which they lost four times, with the points gap to league leaders Atletico Madrid reaching double figures.
However, a remarkable turnaround in form saw Barca swoop up 51 points from a run of 19 matches and if they win their remaining fixtures this campaign, they will be crowned as league champions.
The side are currently third in the standings but will go top if they win their game in hand against Granada on Thursday evening.
Koeman told his pre-match press conference on Wednesday, in quotes carried by El Mundo Deportivo: “The team that is first in La Liga is the favourite to win the league and we are not the favourite yet.
“This game is important because we can be leaders but first we have to win.
“We did not expect to be fighting for La Liga title, but this is our achievement and we will fight for it.
“The team that wants to be champion will have to win all the games that remain this season.
“I see my players as being very strong mentally. I’ve seen the team as being very focused, I don’t see them as believing that the job is done.”