It has been reported that the former Cagliari boss will be shown the door if the Rossoneri do not overhaul Serie A leaders Juventus over the course of the next three games
However, Allegri has dismissed the rumours that Milan owner Silvio Berlusconi and CEO Adriano Galliani are considering firing him.
"I will be the coach of Milan next season," he is quoted as saying by La Gazzetta dello Sport. "I'm 100 per cent sure about that.
"Berlusconi told me again this morning that he's satisfied with my work, and I don't think that he also needs to say it publicly."
Milan are currently second in the Serie A standings, three points behind Juventus with just three games remaining.
The Bianconeri's resurgence this season has been inspired by Andrea Pirlo and is particularly difficult for Rossoneri fans to take given their club allowed the midfielder to move to Turin on a free transfer last summer.
Allegri has copped a lot of criticism for allowing that to happen but maintains that releasing the Italy international was the right call.
"Pirlo is a great champion, but we have absolutely no regrets whatsoever about him leaving Milan and joining Juventus," the former Cagliari boss stated.
"Pirlo also wanted a three-year extension of his contract, but the board wouldn't give him that."
"Besides, he needed new challenges to motivate him. Perhaps he wouldn't have had such a good season if he had stayed at Milan."
Milan will be hoping to keep up the pressure on league leaders Juve when they tackle Atalanta at the Giuseppe Meazza on Wednesday.