Answer:
The short answer is no. If the pregnancy test is negative, you are not pregnant, and therefore you cannot have an ectopic pregnancy.
The long answer is somewhat more complex. There have been case reports in the medical literature of women with demonstrated ectopic pregnancy that had negative urine and even blood pregnancy tests. It is uncertain why this occurred in these circumstances, but it should be noted that this is VERY RARE.
For the overwhelming majority of women, a negative pregnancy test means ectopic pregnancy is an impossibility.