Measuring a weak gravitational lensing signal to the level required by the next generation of space-based surveys demands exquisite reconstruction of the point-spread function (PSF). However, unresolved binary stars can significantly distort the PSF shape. In an effort to mitigate this bias, we aim at detecting unresolved binaries in realistic Euclid stellar populations. We tested methods in numerical experiments where (i) the PSF shape is known to Euclid requirements across the field of view; and (ii) the PSF shape is unknown. We drew simulated catalogues of PSF shapes for this proof-of-concept paper. Following the Euclid survey plan, the objects were observed four times. We propose three methods to detect unresolved binary stars. The detection is based on the systematic and correlated biases between exposures of the same object. One method is a simple correlation analysis, while the two others use supervised machin-elearning algorithms (random forest and artificial neural network). In both experiments, we demonstrate the ability of our methods to detect unresolved binary stars in simulated catalogues. The performance depends on the level of prior knowledge of the PSF shape and the shape measurement errors. Good detection performances are observed in both experiments. Full complexity, in terms of the images and the survey design, is not included, but key aspects of a more mature pipeline are discussed. Finding unresolved binaries in objects used for PSF reconstruction increases the quality of the PSF determination at arbitrary positions. We show, using di ff erent approaches, that we are able to detect at least binary stars that are most damaging for the PSF reconstruction process.