Milan chief executive Adriano Galliani will meet Massimiliano Allegri on Wednesday to discuss the coach's future.
The club ensured their place in next season's UEFA Champions League when they came from behind to beat Siena on Sunday.
Mario Balotelli and Philippe Mexes both scored in the last 10 minutes to secure a 2-1 win, while Fiorentina missed out despite a 5-1 hammering of Pescara.
Despite confirming their place in Europe's premier club competition after a dreadful start to the season, Allegri's future has remained in doubt.
And Galliani, while happy with claiming third place, intends to meet with the coach to discuss the future.
"I will speak to Allegri on Wednesday," the 68-year-old told Tuttosport.
"I feel so cheerful, on Wednesday I will understand what he (Allegri) wants to do. Along with the president, we will make a decision in the light of what he thinks.
"There is a vast difference between the Champions and Europa League. It's like a team that goes from Serie A to B. For that reason there is a lot of tension between third and fourth place."
Meanwhile, midfielder Riccardo Montolivo wants the manager to stay at San Siro.
"I hope Allegri can stay because I think he deserves it, since he led us to this great comeback, but then other factors I can't manage suddenly meddle in."