Senegal qualified for the African showpiece without a defeat, winning five games and drawing one to emerge as Group A leaders with 10 points.
The impressive performances earned them top spot as the best football nation in Africa and 23rd in the world on the last Fifa ranking release.
The Terenga Lions have never clinched the African title, with their best performance being the 2002 edition where they finished as runners-up after losing on penalties to Cameroon.
"I do not think we are favourites. Even if today we are first in Africa in the Fifa rankings, we must not forget that we have never won anything,” Konate told Sport 221.
“Do not hide behind that. You just have to keep your head on your shoulders. We must go to the Afcon with our heads up and focus on the training to be able to do well in the Africa Cup.
“It's after, we know if we're favourites or not. For the last competitions, we did not have enough experience. Today, young players are in our team as well as more maturity in the team. With this mixture, we can do a lot."
Senegal kicked off their preparations for the Afcon with a 7-0 thumping of Spanish-based club Real Murcia on Tuesday.
Aliou Cisse’s men will lock horns against West African neighbours Nigeria in their last build-up game on Sunday.
On July 1, they will wrap up their Group C games against Kenya.