Victory against Parma last time out in Serie A was Milan's first victory since the league's resumption in January, but was only enough to take them up to eighth.
They remain five points off a European spot, while any hopes of securing continental football through the Coppa Italia were ended in the quarter-finals by Lazio.
Reports of Inzaghi's impending sack have been rife in Italy, with suggestions he has been tasked with securing a UEFA Europa League place at minimum - or pay with his job.
But Galliani is sure that Inzaghi will be given time to prove his worth after discussions with club supremo Silvio Berlusconi.
"The president called Inzaghi and myself after he read the reports," Galliani said at an event to welcome January signings Mattia Destro, Gabriel Paletta and Salvatore Bocchetti to Milan.
"What was written was the opposite of what he thinks. He said that Pippo will get experience, none of us has ever said that he won't stay.
"Inzaghi has a contract for next year, and there are no ultimatums. There are 17 games left, we'll try do well, I still don't understand this team."
Destro also spoke at the presentation and was glowing in his assessment of Galliani after the CEO was pictured having travelled to the striker's house in Rome to secure a deal.
"Milan are Milan, there was no convincing needed," Destro beamed.
"I want to do well, and this is the perfect place to do it.
"There were a lot of things which were important in me coming here, but I think Galliani's gesture is the thing that meant the most to me.
"When they told me, I was in disbelief.
"It's nice that he came to Rome to meet me. He's a very important person in the world of football, and it's good that he'd do something like that for me."
