Conflict of interest -- recommendation letters
You cannot incur a conflict of interest within someone other than yourself. In the situation you describe, the only person in jeopardy of a conflict of interest is the professor.
This professor might have a conflict of interest if the professor were to be both a &quot;recommender&quot; and also someone who &quot;asked&quot; you to apply to the professor's department. That is not your concern, since you obviously are not familiar with the details of your school's rules on ethics—the faculty at your school has seen this same situation hundreds of times, and the institution will have well-demarcated guidelines which tell professors how to handle these things.
(I am puzzled regarding two things

how is this professor a &quot;recommender&quot; without also already being committed to writing you a &quot;recommendation&quot;
the difference between being a &quot;recommender&quot; and someone who recommends (someone who &quot;asked [you]&quot;) that you apply to a certain department's program.

Perhaps you are referring to the professor as having some formal status as a Recommender. If that's the case, it is unclear. Anyone can be a recommender, but only a few are Recommenders.)
Do what you will, and if there is any potential conflict of interest for the professor, that is for the professor to resolve. It is not your responsibility.