Fiorentina are into the Europa Conference League final, while Atalanta are in the Europa League final.
Buffon said: "We have shown that we are very competitive in Europe in recent years, even without winning trophies. Fiorentina and Atalanta deserve to seal this season with a trophy.
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"There are all the bases to return to winning ways. I hope that the clubs and their fans can celebrate."
On the Italian national team, the Azzurri team manager added: "We are aware of being competitive, with a super coach and many players who have great love for the Azzurri shirt."