The Chesed L'Avraham (Rebbe Avraham of Radomsk zt'l) states that Zos Chanukah is mesugal for hastening the redemption because this day we read ביום המזבח חנוכת וזאת אותו המשח (Bamidbar 7:84) and המשח is similar to the word משיח.
Another hint to משיח is from שמונת מדליקין חנוכה ימי. The first letters spell משיח. The gematriya of the letters ש"נגה on the dreidel is משיח.
It states in this week's parashah (41:14) וישלח הבור מן ויריצהו יוסף את ויקרא פרעה, "Pharaoh summoned, and he called Yosef, and he was rushed out of the dungeon." The Siforno writes, "[Yosef was saved quickly, as it states ויריצוהו, they rushed him out], like all of Hashem's salvations that happen quickly and immediately. As it states (Yeshayah 56:1), כי לבוא ישועתי קרובה, 'My salvation is near.' This is what happened in Mitzrayim, as it states (Shemos 12:39) ממצרים גרשו כי, 'they were banished from Mitzrayim.' Chazal tell us that their dough didn’t have time to rise before the King of kings, Hakadosh Baruch, redeemed them. This will also occur in the future, as it states (Malachi 3:1), אתם אשר האדון היכלו אל יבוא ופתאום מבקשים, 'Suddenly, he will come to his heichal, the master (Moshiach) whom you await.' May it be speedily in our days.
