There are two kinds of "loop antennas". There are resonant loops, which are loops where the length of the loop is long enough to be resonant. These can be considered folded dipoles, which have been folded into a loop.
A quite distinct antenna is the small loop. These antennas have a perimeter that is electrically small, meaning less than one-tenth of the wavelength.
The two are quite different. The small loop has nulls in two directions perpendicular to the plane of the loop. The resonant loop has nulls in two directions on the plane of the loop. The small loop has a highly inductive impedance. The resonant loop has a purely resistive impedance.
Anyhow, small loops are frequently used for direction finding at HF because they are small and easy to construct. They are quite inefficient antennas, but it's easy to make low-noise amplifiers at HF which can make up for the low efficiency and poor impedance match.
The electrically small loop can be made physically smaller in three ways:
- Make more turns of wire. A small loop with two turns encircling area $A$ is equivalent to a larger loop with one turn encircling area $2A$.
- Increase the permittivity of the space encircled by the loop. For example, by winding the loop around a ferrite material.
- Just make it smaller. Decreasing the area encircled by the loop reduces the antenna's efficiency and sensitivity, but provided the signal is still above the noise floor, this isn't a problem. The small loop wasn't very efficient or sensitive to begin, anyway.
An example of an antenna that does both of these things, and most likely the type of antenna employed by your AM receiver, is a loopstick antenna. These consist of very many turns around a high-permittivity ferrite rod. In doing so, they make the antenna appear electrically much bigger than it is physically.
However, I doubt you will meet success with either of these techniques at 2m. Adding more turns increases the DC resistance, and thus loss of an already not very sensitive antenna. Low noise amplifiers to overcome this are easy at low frequencies, but not at 2m. Also, ferrite materials are lossier with increasing frequency.
On the other hand, you may not need to employ such techniques. An electrically small antenna at 2m is only $2\mathrm{m}/10 = 20\mathrm{cm}$ or less. It's already pretty small.