Cellino hired former Rotherham United boss Evans in October on a contract until the end of the season, and the 53-year-old guided the Whites away from the Championship's drop zone to a 13th-place finish.
Leeds finished the season well with just one defeat in six, but Cellino, who has appointed six managers in two season since taking over at Leeds, merely said that Evans has done the job that was expected of him.
"Steve did the job he was taken on for," the Italian told The Mirror. "He signed a contract until the end of the current season.
"Now I need to know from the shareholders what programme they want from me for next season.
"Believe me, I'm not ready at this moment to give any answer. I need one or two weeks to cool down and focus better."