Your old outlet is a non-grounded 2-prong outlet. You cannot (by code) replace it with a 3-prong. The problem is that anyone using the outlet would have the false impression that it is a grounded outlet.
There are 2-prong outlets available for a direct replacement.
Or you could have a ground wire run to the oulet from the main electrical box ground bus.
Hint: do not use the push-in connections. Use the screw terminals for a better connection.
Good Luck!