An increasing number of brick-and-mortar retailers are expanding their channels to the online domain, transforming them into multi-channel retailers. This transition emphasizes the need for cross-channel recommender systems, aiming to enhance revenue across both offline and online channels. Given that each retail channel represents a separate domain with a unique context, this can be regarded as a cross-domain recommendation (CDR). However, the existing studies on CDR did not address the scenarios where both users and items partially overlap across multi-retail channels which we define as "cross-channel retail recommendation (CCRR)". This paper introduces our original work on CCRR using real-world datasets from a multi-channel retail store. Specifically, (1) we present significant challenges in integrating user preferences across both channels. (2) Accordingly, we propose a novel model for CCRR using a channel-wise attention mechanism to capture different user preferences for the same item on each channel. We empirically validate our model's superiority in addressing CCRR over existing models. (3) Finally, we offer implications for future research on CCRR, delving into our experiment results.