||Feature selection is essential to the field of machine learning, since its application results in an enhancement in training time as well as prediction error of machine learning models. The main problem of feature selection algorithms is their reliance on feature importance estimation, which requires the training of models and is therefore expensive computationally. To overcome this issue, we propose MetaLFI, a meta-learning system that predicts feature importance for classification tasks prior to model training: We design and implement MetaLFI by interpreting feature importance estimation as a regression task, where meta-models are trained on meta-data sets to predict feature importance for unseen classification tasks. MetaLFI calculates a meta-data set by characterizing base features using meta-features and quantifying their respective importance using model-agnostic feature importance measures as meta-targets. We evaluate our approach using 28 real-world data sets in order to answer essential research questions concerning the effectiveness of proposed meta-features and the predictability of meta-targets. Additionally, we compare feature rankings put out by MetaLFI to other feature ranking methods, by using them as feature selection methods. Based on our evaluation results, we conclude that the prediction of feature importance is a computationally cheap alternative for model-agnostic feature importance measures.