Milan are eighth in Serie A after a campaign containing numerous highs such as home wins against Lazio and Napoli and a scoreless draw at second placed AS Roma.
Yet there have also been several low points including three losses in four games after the Christmas break, which has left them on 29 points five adrift of Sampdoria, who occupy fifth place and the final certain Europa League qualifying spot.
Both Galliani and owner Silvio Berlusconi had implied in recent days that if Inzaghi wants to hold on to his job he has to find a way to make it into the top five.
Yet Galliani has changed his tune and says his manager's future is secure.
"He's (Inzaghi) under contract for next season and we intend to keep him here. Whether we qualify for Europe or not," he told a news conference on Thursday.
Should he change his mind, however, the manager most likely to replace Inzaghi is Fiorentina boss Vincenzo Montella, whose teams have produced the kind of attacking football that Berlusconi has always cherished.
A Milan victory at Juventus would certainly boost the team's morale for the remainder of the Serie A campaign.
The two sides traded blows in September until Carlos Tevez was able to break the deadlock in the 71st minute to hand victory to the champions of the last three seasons.
A win for Milan would also be a fillip for second place Roma, who visit Cagliari on Sunday (1400) and are seven points adrift after four straight draws in Serie A.
Rudi Garcia's Roma were eliminated in the Italian Cup quarter-finals on Tuesday in a 2-0 defeat to Fiorentina since when recently-signed forward Victor Ibarbo has been added to an increasing injury list.
Resurgent Napoli are third and only four points behind Roma, having won three games in a row.
Rafa Benitez's side, who host mid-table Udinese on Sunday (1400), booked a place in the domestic cup semi-finals on Wednesday, after beating Inter Milan with a late goal from Gonzalo Higuain.
Sampdoria, still seething from Sunday's 5-1 thrashing at Torino, face dangerous Sassuolo (Sunday 1400), while fourth-place Lazio play on Monday (1945) against Genoa at the Stadio Olimpico.
(Editing by Toby Davis)
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