If you are on a scholarship at your current school (NCAA D1, D2?) and looking to lateral transfer or transfer up to another school then you will (eventually) need a release from your current school to be eligible at the new school. If you don't get a release, then you can expect to "red-shirt" a season at the new school before becoming eligible to compete again. If this other school is in the same conference or a regular competitor with your current school, then they may be less motivated to grant the release.
If you transfer down (D1>D2>D3), then you don't need a release.
If you aren't on scholarship, then this should be much less of an issue.
Excuse me for giving conflicting advice, and I may be wrong about this, but you don't want to "poison the well" with your current coach until you know you will be admitted (and when) at another school. If a coach at the new school can't/won't talk to you because of NCAA rules, they will let you know. It's best for you to do the leg-work to find out what school is a better fit for you and apply and get admitted so then you have an option and a decision to make.
Most coaches would want to know sooner than later what your plans are as far as continuing with the team (or being on a scholarship), but until you know for sure that you have a better option then you are better off keeping a low profile. If you coach finds he has another scholarship to award when a new season starts, he can offer it to current walk-on athlete if it's passed the recruiting window.
It's OK to say that your educational goals will be better met by the new school for your reason to change schools, and most people will understand.
Finally, if you are unhappy with your current school but unsure of where you want to go next, look into transferring to a community college that has a XC/track program and transfer agreements with other schools.