Speculation has mounted that Mazzarri will be sacked if the Milan outfit miss out on a place in the UEFA Europa League.
Fassone has stressed the importance of Inter, who occupy fifth place with five games of the season remaining, securing European football for the 2014-15 campaign, but backed former Napoli coach Mazzarri to take the club forward regardless of what they achieve this season.
"The Europa League is not a hidden goal. Inter must be in a cup after a year without," Fassone told Sky Sport Italia.
"The coach has been asked to take the team as high as possible; he is doing a great job and I have already mentioned to him that we are planning for the future.
"It will certainly involve Mazzarri. And specifically there is no correlation between his tenure and qualifying for Europe. A possible renewal then? Of course, we will talk.
"We don't set ourselves targets, but the competitions we play in need Inter to be prominent, we won't trot out excuses.
"Inter need to be competitive on the pitch, within the timeframe it typically takes between the end of one cycle and the beginning of another."
Inter face a crunch clash at sixth-placed Parma on Saturday as the battle for a Europa League spot hots up.
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