This paper describes an audio-visual speech enhancement (AV-SE) method that estimates from noisy input audio a mixture of the speech of the speaker appearing in an input video (on-screen target speech) and of a selected speaker not appearing in the video (off-screen target speech). Although conventional AV-SE methods have suppressed all off-screen sounds, it is necessary to listen to a specific pre-known speaker's speech (e.g., family member's voice and announcements in stations) in future applications of AV-SE (e.g., hearing aids), even when users' sight does not capture the speaker. To overcome this limitation, we extract a visual clue for the on-screen target speech from the input video and a voiceprint clue for the off-screen one from a pre-recorded speech of the speaker. Two clues from different domains are integrated as an audio-visual clue, and the proposed model directly estimates the target mixture. To improve the estimation accuracy, we introduce a temporal attention mechanism for the voiceprint clue and propose a training strategy called the muting strategy. Experimental results show that our method outperforms a baseline method that uses the state-of-the-art AV-SE and speaker extraction methods individually in terms of estimation accuracy and computational efficiency.