How to respond to "what you can bring to our department" in reply of a sabbatical request? I am a faculty member at a university in a developing country. I love my field of research very much and want to improve my knowledge and level of expertise. I did worked always by myself and without being in touch with any other researcher in my field. Nearly a week ago, I sent a letter to one of the leading researchers (top 10) in my field to accept me for a sabbatical program and attached to the email one of my papers which is 15 months under review in a prestigious journal. The main reason for asking for sabbatical is that I really don't know what direction to go from here, in my journey in research. 

Fortunately, their secretary answered me that we are full and don't have the space to host you, but we will look if we can find a solution and meanwhile send a cv. 
A day after I sent my cv, she mailed me to make a proposal for the project you want to do here, with whom you want to collaborate and what you will bring to the team here, and why you need to come in order to do the project.

These are perfect questions for a researcher to answer, but given that I don't have a sense of research direction, the importance of problems, and don't know what are important problems right now. I really want them to help me with the project. Even I prefer them to set a direction of research for me.

Given that I want to escape out of my bubble I'm in and connect with leading researchers, what they want me to tell for the question of what you could bring to here?
This all sounds like they are interested in you for a reason you don't state and may not know. Laboring alone is difficult, but in some cases it has proved especially beneficial. The case of Srinivasa Ramanujan is instructive. Perhaps you have shown them something in your CV that they haven't considered and might find valuable. A sole researcher will occasionally develop new patterns of thought that are unknown to others. 

But, I think you need to do a bit of research on that department if you haven't already. Who there would you want to work with and why. You need some familiarity with their work. 

You want to extend your range and so do they. If your past results are interesting (to them, primarily) you could offer to conduct a seminar focused on insights for faculty and advanced students. This would be thought valuable. And you could also participate in seminars of other, targeted, faculty. 

But you need to first understand what they do and how what you have done can enhance that in some way. Then, they might be able to overcome the lack of a slot for a visitor.