According to Iyun Yaakov, Yosef Lekach, Rashi, and the Vilna Gaon, the advisers were advising Haman to beg Mordechai for forgiveness.
Furthermore, as the Alshich points out, the Talmud (Yevamos 79b) defines Jews as rachmanim, merciful by nature. Therefore, Mordechai would forgive Haman. Having no other choice, Haman would eventually listen (Esther 7:8), and beg Esther for his life.
R’ Moshe ibn Habib is quoted in Dena Pishra as saying that the advisers were suspicious that Esther was Jewish because she decreed that all barbershops were to be closed. Therefore, they advised that Haman beg Achashverosh for forgiveness and revoke the decree against the Jews.
Perhaps they also intended that knowing Esther’s origins – a topic concerning which the king had not yet been satisfied – could be an effective advantage to Haman in having influence on Achashverosh.
The Malbim says the advisers suggested that Haman make Mordechai overconfident with continued honors, so he would stop praying and fasting. They clearly did not know that Mordechai went back to sackcloth and ashes immediately upon his return from the display of honor Mordechai perceived as merely a dog and pony show.