The Rossoneri have faltered in recent weeks as a 2-2 draw at Torino was followed up by last weekend's 2-1 home loss to Napoli, meaning they have won just once in five league matches to drop to seventh.
Milan were also knocked out of the Coppa Italia by Juventus in midweek, but put in a spirited performance in the 2-1 loss, having played the majority of the second half with 10 men due to Manuel Locatelli's red card.
Deulofeu made his first appearance since joining on loan from Everton off the bench in that match and the winger put in a lively cameo.
Head coach Montella is contemplating putting the Spaniard in from the start against Udinese and says it his job to get the best out of Deulofeu and the squad as a whole as they attempt to get their bid for Champions League football back on track.
"It is possible that Deulofeu will start [against Udinese]," he told a news conference. "He is someone who has always been predestined for greatness.
"We have to understand why he has not yet achieved that level. My job is to get the best out of him."
On Milan's form, he added: "We have to act as if our season starts tomorrow and above all be a mature side.
"It takes time. The first phase of the season went well, now we start phase two.
"The last two games we did not start with the wrong attitude, but we paid for the ability of our opponents."