Should I mention potential collaborative opportunities in my research statement?
I presume this is job interviews in academic positions.

The appropriate place to mention such possibilities is only in your proposed research plan. When you do state names, state where the person is located and what role that person is to play in the collaboration. 

Example

Defining the Role of Cats in Human Mental Health

For this project, I will ... bla ... bla ...


Potential Research Collaborations


Dr. Joe Smith, Sociology Department, Pet Friendly University, Cat Heaven, USA (123) 456-7890, j.smith@...
As a renowned cat psychologist, Dr. Smith will contribute his expertise to evaluate whether the cats are happy during the study. We plan to jointly supervise the graduate student on this project.
Dr. Alice B. Nice, ...

Potential Research Funding Sources


The Society for Improved Mental Health (SIMH)
...



Certainly, you will have vetted all of your statements that you make with each of the potential collaborators BEFORE you submit your document for the job applications. We on the other side of the interview will be contacting Dr. Smith as demands warrant!