Inzaghi was heavily linked with a money-spinning move to Al Hilal just before they were set to kick off their Champions League final game against PSG.
The Italian giants went on to lose 5-0, the most comprehensive defeat in a final in the competition’s long history.
Not long after the defeat, Inzaghi ultimately decided to leave the club, something that Dumfries, 29, revealed the squad spoke about.
In an interview to Gazzetta Dello Sport, he said: "It was very difficult for me and for everyone, we were very close to Inzaghi. I arrived here at Inter with him, everything I built at Inter was with him. For four years we were like a family.
"The rumours did not influence us in the preparation for the final, but it is clear that we were reading. We heard rumours that we carried inside, but without talking about them among ourselves because everyone was focused only on the final. I assure you that in our heads there was only PSG and nothing else.
"My Inter dream is simple: to win the Champions League, the only thing missing. I'd like to bring the trophy to Milan and celebrate it in a sea of fans like I did with the second star."