Ytdyklly

I, a graduate student, have started tutoring undergraduates in computer science at my university to help make ends meet. One student who inquired about my services turned me down upon hearing my rates and remarked (in writing) that they might as well just buy solutions to their projects on a particular freelancing website for that price, as their friends do.

Should I tell the professor about this student, in case he wants to review their submissions more closely? I don't have any proof that they have already cheated, but this constitutes strong evidence that they are likely to. In this question, the OP appears to have evidence to suggest that cheating has taken place already, which seems more clear-cut.

In dubio pro reo. Evaluations of projects is already a highly subjective process. If you tell someone "Please evaluate this project, it is very likely the author cheated" they will probably give a worse grade than if simply told to evaluate the exact same project. What if the student then didn't cheat?

If your institution has no way of properly assessing a candidate, i.e., one could "buy" a degree by having external services do the work, then this is an institutional problem and you won't fix it by suggesting to a professor that one of their students may cheat.

Lastly, think about the effects your behavior has on the institutional climate. Would you like to study in an environment in which people tell professors "Arnold may be cheating, I watched him visit that freelancing website"?

[The student] remarked (in writing) that they might as well just buy solutions to their projects on a particular freelancing website for that price, as their friends do.

That does not sound to me like "admitting" that they "would" cheat. If I said to a prospective financial advisor, "your rates are so high I may as well just declare bankruptcy now", that does not mean that I am going to declare bankruptcy, it is merely a way to express that the advisor's services do not seem cost-effective.

Given this, I would do nothing -- you offered legitimate tutoring services and the student declined your offer. You have no compelling reason to suspect that the student will actually cheat.

First, I'll guess that the prof already recognizes the possibility.

Second, if you have a contractual obligation to the student you need to honor it. I doubt that is the case here since you were turned down. But you can't, ethically, act against the interests of your clients. You can, of course, back out of a client relationship if you think the client is abusing it or otherwise acting unethically.

Don't interpret the above to imply that you must do what the client wants you to do if it is unethical. Some relationships are governed by law, but those laws, i think, just try to codify what good ethics suggests. Lawyer-client relationships for example have legal constraints.

But even in the case you have such an obligation, you still could inform the prof that you have some evidence that such cheating is being contemplated. If asked by who, you may need to decline to answer. In particular, naming a student may well be very unfair as the student might just have been expressing frustration out loud, with no intent to break the rules.

If the prof is a bit naive, you can inform him/her about the likely web-sites that enable such things. But it is the professors responsibility to "police" the class.

No. It's not your job to worry about that.