Traditional active learning tries to identify instances for which the acquisition of the label increases model performance under budget constraints. Less research has been devoted to the task of actively acquiring feature values, whereupon both the instance and the feature must be selected intelligently and even less to a scenario where the instances arrive in a stream with feature drift. We propose an active feature acquisition strategy for data streams with feature drift, as well as an active feature acquisition evaluation framework. We also implement a baseline that chooses features randomly and compare the random approach against eight different methods in a scenario where we can acquire at most one feature at the time per instance and where all features are considered to cost the same. Our initial experiments on 9 different data sets, with 7 different degrees of missing features and 8 different budgets show that our developed methods outperform the random acquisition on 7 data sets and have a comparable performance on the remaining two. © 2020, The Author(s).