How to approach other professors in a department when the potential advisor is unsure of his funding situation? I am a M.Sc. graduated in Computer Science and I am going to continue my graduate studies abroad. There is one professor who I am in contact for a few months and now he states that he is willing to hire me as PhD student if he receives good news of the grant proposals that he submitted to funding organizations. However, there is another professor in that department that I think we have a considerable overlap in our interests and backgrounds too. I mentioned the name of those professors in my Application Form in order. So now, how can I let the second professor knows (e.g. by email) that I am serious about joining her lab if the first professor could not provide funding for me. I should mention that In this department, there is just a formality admission committee and professors (independently) hire students if they can support their students through sources of funds.
The simplest solution seems to be the best - just be honest with both. Everybody knows that funding can be very difficult, and no one would blame you for having more than one horse in the race. It is, in fact, expected of a good student to seek out options. But we can consider some options.

Logically there are four options. You discuss with both, you discuss with neither, you discuss only with your first priority (called A) or you discuss only with your second priority (called B).

Discuss with neither: Nothing good will come out of this - they cannot read minds, and don't know your intentions if you don't speak up.

Discuss only with A: If A's funding falls through, this risks becoming awkward with B. You don't, in fact, know if B for example has other plans if you don't discuss it.

Discuss only with B: If A's funding falls through and you get a place at B's team, this may be awkward as you still have to be in the same department as A.

Now ask yourself - are there any downsides from discussing with both? I cannot think of any.