I am currently looking for a PhD-position and I am in touch with a professor already for some weeks. We had two zoom meetings and discussed about possible topics. The official call for the application starts soon. The professor now also said that he helps me writing the research proposal.
Now, within the same research group, there is also another professor, which is doing research in quite some different direction. I also wrote him an email some time ago (before I become in touch with the prof mentioned above) and he said that he has a free position. Now, I would like to ask him for a meeting in order to discuss about possible topics.
Obviously, I can only apply once for the same university, but still I would like to know about all possibilities. Now, my question is the following: Is it "impolite" or "ungratful" to ask the second professor for available topics? I do not want to give the first professor the feeling that I do not like his topic and I am looking for something better, because in fact, I really like his research program. As I say, I just would like to see all possibilites before applying.