In animal breeding, parents of the next generation are usually selected in multiple stages, and the initial stages of this selection are called preselection. Preselection reduces the information available for subsequent evaluation of preselected animals and this sometimes leads to bias. The objective of this study was to establish the minimum information required to subsequently evaluate genomically preselected animals without bias arising from preselection, with single‐step genomic best linear unbiased prediction (ssGBLUP). We simulated a nucleus of a breeding program in which a recent population of 15 generations was produced. In each generation, parents of the next generation were selected in a single‐stage selection based on pedigree BLUP. However, in generation 15, 10% of male and 15% of female offspring were preselected on their genomic estimated breeding values (GEBV). These GEBV were estimated using ssGBLUP, including the pedigree of all animals in generations 0–15, genotypes of all animals in generations 13–15 and phenotypes of all animals in generations 11–14. In subsequent ssGBLUP evaluation of these preselected animals, genotypes and phenotypes from various groups of animals were excluded one after another. We found that GEBV of the preselected animals were only estimated without preselection bias when genotypes and phenotypes of all animals in generations 13 and 14 and of the preselected animals were included in the subsequent evaluation. We also found that genotypes of the animals discarded at preselection only helped in reducing preselection bias in GEBV of their preselected sibs when genotypes of their parents were absent or excluded from the subsequent evaluation. We concluded that to prevent preselection bias in subsequent ssGBLUP evaluation of genomically preselected animals, information representative of the reference data used in the evaluation at preselection and genotypes and phenotypes of the preselected animals are needed in the subsequent evaluation.