You can for a short time, but not permanently.
Energy is conserved. It can change from one form to another, but you can't create it or destroy it. Potential energy is is one form of energy. Kinetic energy is another. An electric current is moving electrons. It also contains a form of energy.
Suppose you have two magnets separate by a short distance. One is glued down and the other is free to move. They attract. Magnetic forces propel the free magnet to the fixed magnetic. It gains speed and kinetic energy.
Now repeat the experiment, but add a loop of wire. The free magnet passes through the loop on the way to the fixed magnet. The wire loop experiences a changing magnetic field as the magnet passes by. Changing magnetic fields exert forces on charges. Wires have electrons that can freely move within the wire. Moving electrons is a current. So this time the moving magnet generates a current.
But this only lasts for a moment. The free magnet hits the stationary magnet. The collision bumps atoms in both, causing them to vibrate a little harder. Kinetic energy has been changed to heat.
The moving electrons aren't totally free to move. They bump into atoms of the wire, causing them to vibrate a little harder. Electric energy turns to heat.