Abstract. In this series of papers, we present statistical maps of mirror-mode-like (MM) structures in the magnetosheaths of Mars and Venus and calculate the probability of detecting them in spacecraft data. We aim to study and compare them with the same tools and a similar payload at both planets. We consider their dependence on extreme ultraviolet (EUV) solar flux levels (high and low) and, specific to Mars, on Mars Year (MY) as well as atmospheric seasons (four solar longitudes Ls). We first use magnetic-field-only criteria to detect these structures and present ways to mitigate ambiguities in their nature. In line with many previous studies at Earth, this technique has the advantage of using one instrument (a magnetometer) with good time resolution, facilitating comparisons between planetary and cometary environments. Applied to the magnetometer data of the Mars Atmosphere and Volatile EvolutioN (MAVEN) spacecraft from November 2014 to February 2021 (MY32–MY35), we detect events closely resembling MMs lasting in total more than 170 000 s, corresponding to about 0.1 % of MAVEN's total time spent in the Martian plasma environment. We calculate MM-like occurrences normalised to the spacecraft's residence time during the course of the mission. Detection probabilities are about 1 % at most for any given controlling parameter. In general, MM-like structures appear in two main regions: one behind the shock and the other close to the induced magnetospheric boundary, as expected from theory. Detection probabilities are higher on average in low-solar-EUV conditions, whereas high-solar-EUV conditions see an increase in detections within the magnetospheric tail. We tentatively link the former tendency to two combining effects: the favouring of ion cyclotron waves the closer to perihelion due to plasma beta effects and, possibly, the non-gyrotropy of pickup ion distributions. This study is the first of two on the magnetosheaths of Mars and Venus.