Answer:
No. Asteroids are scattered throughout the solar system in various orbits, some of which are relatively stable. Some have orbits that pass near Earth. But the vast preponderance of large asteroids are in the Main Belt between Mars and Jupiter.
The problem with highly elliptical orbits is that the asteroid will be influenced by the major planets, moons, and the Sun. If its orbit is disturbed, it could be trapped by a giant planet or pulled too close to the Sun. Over the life of the solar system, many small asteroids have been either pulled into the Sun or ejected from the inner solar system by the gravity fields there.