Earlier this week, Tare attempted to calm supporters who were disgruntled that key transfer target Davide Astori had been snared by fierce rivals Roma.
The 41-year-old has now revealed that he has been subject to harassing messages, while also suggesting that fake plane tickets had been booked in his name.
"After that night and the confrontation with the fans over Astori, the trouble really started," he told Il Tempo.
"Someone must've got hold of my phone number, as I found it on the internet. The usual threatening messages started arriving, but not just those.
"There were strange calls, like one from [airline] Alitalia because somebody had booked a flight to Rotterdam in my name. I spent two hours trying to undo it and figure out who had done this.
"Over the next few days I'll be forced to change my phone number again, which won't be an easy task as that is a fundamental instrument in my work.
"Many problems are emerging, but what upsets me the most are the things said to my family."
Lazio fans have previously vented their frustration at owner Claudio Lotito, who in February claimed to have allegedly received death threats for selling Hernanes to Inter.