I would like to use four HC-SR04 ultrasonic sensors within close proximity to each other. Will this cause any interference in the sensor readings.
Yes, of course. You can use only one sensor at a time, and need to wait long enough for the room echos to die down before activating the next sensor.
To add some more perspective to jremington’s comments, the ultrasonic devices are pretty directional so you can certainly work a group of them in close proximity as long as they are not pointing to each other. As an example; you could have, in theory, two devices pointing 180deg away from each other (i.e. back-to-back) - you may need to dampen/isolate the space in between the two devices so the emission/return from one is not “heard” by the other one. Just remember they work in the audio band (so think of them as fairly directional speakers).