The Telegraph is reporting Postecoglou is set to be replaced by chairman Daniel Levy even if they finish the season as Europa League title winners.
In reaction, Bosnich said on SEN Radio in Australia: "Sometimes the rumours are actually put out by the clubs themselves to give the manager and team a kick up the pants.
"It has been a poor season no doubt about that....18 defeats for a team of Tottenham's stature is not good enough.
"But I will say this to all Spurs fans....forget about the (Premier) League right now. You are not going to get relegated.
"And in terms of Ange, if he's going to go down, he's going to go down fighting. I think sacking him would be extremely harsh (even if they win the Europa League)."
'I can understand the hurt and disappointment, but they have just got to stick with it until the end of the season."