The FCC will permit a construction permit to be assigned to a different organization as long as 18 months since the grant of the construction permit has passed. The caveat though is that if the construction permit is assigned to a different organization, they will only have the remaining time of the original 3 year permit. They can't seek an extension except for a natural disaster or other specific event that would qualify for tolling.
Keep in mind that the assignment process normally takes about 45 to 60 days to get a grant from the FCC. Therefore, there must be plenty of time remaining in order to achieve the grant of the assignment, consummate the transaction and build the facility. If the facility is not going to be built at the same location, then you must first seek a modification of the construction permit (this can take place during the assignment process).
If the permit only has about 3 months on it, it's not even worth trying.