Thompson was optioned to Triple-A El Paso on Wednesday.
Thompson began spring training at major-league camp and allowed four runs on four hits and two walks while striking out two over 2.1 innings during four three relief appearances this spring. The right-hander's contract was selected by the Padres in November to protect him from the Rule 5 draft, and it appears as though he'll advance to the Triple-A level to begin the year.