Neither PO nor Scrum Master is responsible, but the team is supposed to conduct daily standups. As a Scrum Master its your job to facilitate the team and make sure that process is being followed. Coach them to make the standups effective as opposed to having just mechanical updates during the daily ritual.
The Scrum Master ensures that the Development Team has the meeting, but the Development Team is responsible for conducting the Daily Scrum. The Scrum Master teaches the Development Team to keep the Daily Scrum within the 15-minute time-box.
Daily scrum is an important information radiator for the team. They have made a commitment to deliver agreed upon tasks during a time-boxed duration. Daily standup meetings help the team in tracking its progress with reference to their commitment. These meeting may or may not provide much value to other stakeholders and PO, which is why presence of PO is not mandatory in Scrum daily standups.
The daily scrum meeting is not a status update meeting in which a boss is collecting information about who is behind schedule. Rather, it is a meeting in which team members make commitments to each other.
In your case, the PO may be getting involved because just to fill the void left by the team. Instead of talking to the PO, talk to the team first. Make them aware that its their job and why is it important. They should be running these meetings, so just in case if both PO and Scrum Master are not present on a particular day, the standup should be equally effective and efficient without them.
The Daily Scrum is intended to disrupt old habits of working separately. Members should remain vigilant for signs of the old approach. For example, looking only at the ScrumMaster when speaking is one symptom that the team hasn’t learned to operate as a self-organizing entity.