I applied for a software position in a large, reputed company and was contacted to schedule phone interviews. They asked me to provide a few dates over the next 3 weeks so that they could schedule these interviews. I followed up with them after a week of no response, and they told me they would get back to me with a save-the-date email as soon as possible. I followed up with them again after 3 weeks, and even provided a bunch of new dates.
Meanwhile, I am also applying to other companies, and have had interviews or have interviews scheduled with them. However, I am particularly keen on interviewing with the company I mentioned earlier. I am worried that the interviews may not be scheduled in time, and I may have to accept another offer if it is delayed a lot.
I did mention in the initial e-mail that I am actively looking for jobs. However, I did not have any interviews scheduled at that particular time, so I did not think it was necessary to mention them.
Is there a way in which I could push for these interviews to be scheduled soon, without seeming rude or inconsiderate? I understand that it is of low priority to them, but I do not want to lose this opportunity.