How to ask for an academic agreement with a foreign faculty?
Setting up a formal relationship between departments can be a lot of work, and requires strong motivation on both sides.  

A possible lighter-weight option to consider would be a more unidirectional program like exists at the department of one of my colleagues in Europe.  In his institution's Ph.D. program, each student is required to do two terms abroad at another institution.  The university supports this by continuing to support the students financially while they are abroad, but it is up to each student and faculty member to arrange where they go and who they work with independently.

As I have observed it in practice (i.e., being on the other end hosting a visiting student), this it much easier for others to agree to than a formal arrangement between faculties, because it requires fairly little investment and are likely to be covered by normal "visiting scholar / visiting student" arrangements.  It's also a great way to bootstrap collaboration with a foreign colleague.