system
Given the following post, respond as if you're commenting on Reddit:
human
How to gently reject a student?

I apologise in advance if this gets lengthy but I am at a loss as to what to do.

I am the head of my (small) department and I am one of two professors who teach the coursework for our master's program. Because of this I am very familiar with this particular student, let's call her Sarah, and her work.

Sarah is a lovely, friendly girl. She has been eager to assist with conferences, workshops and with the undergrads, although our institution does not allow master's students to teach. Due to her outgoing nature, she feels comfortable coming to me with her academic struggles and I feel as though she's put me in a bind.

Quite frankly, Sarah is underperforming in her master's. I'm not sure how a student managed to do so well in her undergraduate and yet perform so poorly in her master's. I do not take her performance as a reflection on the program as the rest of her cohort is performing as expected.

Sarah struggled the entire year. She had difficulty keeping on top of the coursework and participating in class. She spent a few weeks prior to the exams crying in my office about how she was expecting to fail. She registered with disability services and I had hoped that this would help her, as she was given double the time of the other students for the exams, but alas, after each exam she came to me, in tears, over her performance. Of the four exams, she only completed one. While she managed to pass them, it was only barely. Her cohort scored well above minimums, so again, I do not think it is a reflction of the exams or the program.

Their dissertation is due at the beginning of August, and Sarah emailed me about 2 weeks back to let me know she hasn't even begun. She has had her topic and the necessary materials since late November and this was after 3 months of her being unable to come up with a topic, struggling to write a research proposal and finally, my colleague handing her a project to complete in the hopes that it would calm her nerves and makes things easier for her. Thus far it has not. She continues to come to my office on a nearly weekly basis to express that she does not believe she will finish her dissertation at all, much less by the deadline, and generally, does not believe that she will pass her master's. 

Baffingly, however, she believes that she will be admitted to our PhD program for next year. She has not yet applied, but has come to me to ask about funding on numerous occassions. She doesn't speak about the PhD as if it is a possibility, or an option, but she discusses it as if it is guaranteed. My colleagues have mentioned as well that she speaks to them about it as though she will definitely be accepted. 

The problem is, we would not accept her at this point. Her performance in her master's leaves her with a transcript that is far below our standards, even if she does complete the dissertation which I don't hold out much hope for. Outside of her transcript, I do not believe she could competently complete a PhD. She has demonstrated that she does not understand the material (through her exams) and as she expects she will simply be given a PhD topic (she has already asked me to give her something to work on) and as she has yet to start her master's, I am not confident in her research ability. 

I do not know what to do. I have thus far answered her questions - I told her about the funding situation but emphasised that it is extremely competitive and expressed that I was not comfortable handing her a research topic when our other candidates came up with their's independently. But she keeps talking about her PhD next year. I don't want to crush the girl, but I don't know how to tell her that she isn't a suitable candidate when she hasn't asked about it, or even applied. It feels inappropriate to unofficially reject her, when she hasn't made the official step of an application 

Our master's is terminal, there is no expectation of continuing, and our institution allows PhD applications up until a month before you're intended to begin. 

Any input will be appreciated. Professors who have dealt with similar situations, or students who have been in Sarah's situation and know best how to soften the blow.
gpt
The later you leave it the worse it becomes. Ideally you should have addressed this the very first time she spoke about it as a sure thing.

Be honest and forthright. It's as simple as that. Just be clear. It's not nasty to explain that someones performance puts them below the acceptance level. You let her down in the same way that you let down the unsuccessful candidates after a job interview; politely, clearly, and leave it at that.