An increasing number of retailers are expanding their channels to the offline and online domains, transforming them into multi-channel retailers. This transition emphasizes the need for cross-channel recommendations. Given that each retail channel represents a separate domain with a unique context, this can be regarded as a cross-domain recommendation (CDR). However, 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 a real-world dataset from a multi-channel retail store. Specifically, we study significant challenges in integrating user preferences across both channels and propose a novel model for CCRR using a channel-wise attention mechanism. We empirically validate our model's superiority in addressing CCRR over existing models. Finally, we offer implications for future research on CCRR, delving into our experiment results.