A decision over Evans' future at Elland Road is due after Saturday's final league fixture.
Evans, whose rolling contract expires at the end of the campaign, admitted he expects to learn his fate shortly after Saturday's season finale at Preston North End.
Should the Scot depart, he would be the sixth head coach to be fired during Cellino's reign.
However, Evans insisted his relationship with the Italian is one of mutual respect and added that, by Cellino's own admission, the same cannot be said of those who've gone before him.
"There’s a lot of mutual respect there," the 53-year-old said, as quoted by the Yorkshire Evening Post. "That’s why if we sit down and it’s a negative chat for me, Mr Cellino will tell me.
"By his own admission he’s not told any other head coaches that but he will tell me. I’ll be the first to know either way."
Evans was appointed a matter of hours after his predecessor, Uwe Rosler, was relieved of his duties by Cellino, whose hiring of the German came before an announcement had been made over the future of Neil Redfearn, the previous incumbent.
Speculation over Evans' future has been a constant since day one of his tenure and earlier this week the former Italy goalkeeper Walter Zenga became the latest name to be linked with the Elland Road post.