Strong-field ionization (SFI) has been shown to prepare wave packets with few-femtosecond periods. Here, we explore whether this technique can be extended to the attosecond time scale. We introduce an intuitive model, which is based on the Fourier transform of the subcycle SFI rate, for predicting the bandwidth of ionic states that can be coherently prepared by SFI. The coherent bandwidth decreases considerably with increasing central wavelength of the ionizing pulse but it is much less sensitive to its intensity. Many-body calculations based on time-dependent configuration-interaction singles support these results. The influence of channel interactions and laser-induced dynamics within the ion is discussed. Our results further predict that multicycle femtosecond pulses can coherently prepare subfemtosecond wave packets with higher selectivity and versatility compared to single-cycle pulses with an additional sensitivity to the mutual parity of the prepared states. © 2016 American Physical Society.