Not as such. Even 'global' minor modes are generally just buffer-local minor modes which are enabled or disabled for multiple buffers en masse.
However there's nothing to stop you writing a global mode (or hook function, or whatever approach makes the most sense) which is ostensibly active everywhere, but which checks the window of the current buffer, and only actually does something if that window is the one you're interested in. Or you might determine the buffer currently displayed in the window you're interested in, and do things with that.
That will work nicely for some kinds of behaviours, and be very difficult for others, so it really depends on what you're hoping to achieve.