This study explores the expectations of older adults towards conversational companion robots and provides design recommendations for developing such robots using foundation models. The research involved 28 older adults in participatory design workshops, where they engaged with a companion robot using a large language model (LLM) and discussed scenarios representing everyday situations. Thematic analysis of the discussions revealed that older adults expect conversational companion robots to actively engage in conversations when alone and passively in social settings, remember previous conversations, personalize interactions, protect privacy, provide information and daily reminders, foster social skills, and express empathy and emotions. Based on these findings, the study provides actionable recommendations for designing conversational companion robots for older adults using foundation models such as LLMs and vision-language models. The recommendations emphasize the importance of integrating LLMs for their advanced linguistic capabilities, combined with other state-of-the-art technologies for multimodal aspects. The study also highlights the need for privacy protection, data control, and the ability to provide information and support in various contexts. The findings suggest that companion robots should be designed to foster social connectedness, provide emotional support, and facilitate meaningful interactions with older adults. The study underscores the importance of involving older adults in the design process to ensure that these robots align with their unique expectations and needs.This study explores the expectations of older adults towards conversational companion robots and provides design recommendations for developing such robots using foundation models. The research involved 28 older adults in participatory design workshops, where they engaged with a companion robot using a large language model (LLM) and discussed scenarios representing everyday situations. Thematic analysis of the discussions revealed that older adults expect conversational companion robots to actively engage in conversations when alone and passively in social settings, remember previous conversations, personalize interactions, protect privacy, provide information and daily reminders, foster social skills, and express empathy and emotions. Based on these findings, the study provides actionable recommendations for designing conversational companion robots for older adults using foundation models such as LLMs and vision-language models. The recommendations emphasize the importance of integrating LLMs for their advanced linguistic capabilities, combined with other state-of-the-art technologies for multimodal aspects. The study also highlights the need for privacy protection, data control, and the ability to provide information and support in various contexts. The findings suggest that companion robots should be designed to foster social connectedness, provide emotional support, and facilitate meaningful interactions with older adults. The study underscores the importance of involving older adults in the design process to ensure that these robots align with their unique expectations and needs.