When properly executed within an appropriately-sized Scrum team, the daily stand-up should never take more than 15 minutes or so. If it takes longer, either the team is too big or you have a process problem.
The Purpose of the Stand-Up
The daily stand-up is a commitment and coordination meeting for the entire team. It is designed to ensure that the entire team is aware of impediments, what stories are done or not-done, and what tasks are ready to be pulled from one team member's to-do list into someone else's.
It's important that the Scrum Master and the Product Owner be active participants in the stand-up, but if the team is reporting to either of them then your Scrum process may be well and truly broken. A related answer on Project Management Stack Exchange has a 10-point list of "project smells" at the bottom, some of which may apply in your case. Even if they don't apply, you should definitely re-evaluate the effectiveness of your stand-ups at your next Sprint Retrospective.
Respect the Time-Box
While I dislike the "three questions" as a concrete format precisely because they tend to lead to meetings that resemble a status pull, I'd be remiss if I didn't point to Mike Cohn's canonical description of the Daily Scrum. The page says, in part:
By focusing on what each person accomplished yesterday and will accomplish today, the team gains an excellent understanding of what work has been done and what work remains. 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.
There's a lot more detail and some concrete examples on that page. However, for the purposes of your question, it is explicitly stated that:
Scrum daily standup meetings are strictly time-boxed to 15 minutes. This keeps the discussion brisk but relevant.
The time-box is the foundation of Scrum. While most time-boxes within Scrum can be adjusted by the team as a result of the inspect-and-adapt cycle, it is considered poor practice to extend the length of the stand-up. If the time-boxing principle isn't being respected within your process, that's generally a very whiffy "project smell."