Current methods of cross-lingual parser transfer focus on predicting the best parser for a lowresource target language globally, that is, "at treebank level". In this work, we propose and argue for a novel cross-lingual transfer paradigm: instance-level parser selection (ILPS), and present a proof-of-concept study focused on instance-level selection in the framework of delexicalized parser transfer. Our work is motivated by an empirical observation that different source parsers are the best choice for different Universal POS-sequences (i.e., UPOS sentences) in the target language. We then propose to predict the best parser at the instance level. To this end, we train a supervised regression model, based on the Transformer architecture, to predict parser accuracies for individual POS-sequences. We compare ILPS against two strong single-best parser selection baselines (SBPS): (1) a model that compares POS n-gram distributions between the source and target languages (KL) and ( The results from our extensive evaluation, coupling 42 source parsers and 20 diverse low-resource test languages, show that ILPS outperforms KL and L2V on 13/20 and 14/20 test languages, respectively. Further, we show that by predicting the best parser "at treebank level" (SBPS), using the aggregation of predictions from our instance-level model, we outperform the same baselines on 17/20 and 16/20 test languages.