Is it mandatory that an email address be used as an apple ID? I cannot use my current one and I do not want to establish another email address

There's a few places where you can use a telephone number. Read the link below for more information.

For information about how to 'Use your mobile phone number as your Apple ID', click here --> Use your mobile phone number as your Apple ID - Apple Support

"When you create a new Apple ID in some countries or regions, you can use your mobile phone number as your Apple ID username."

"If you already have an Apple ID that's an email address, you might not be able to change it to a mobile phone number. However, you can associate your account with different phone numbers or email addresses on your Apple ID account page."

Note that it must be a verifiable email address as the process of completing the creation if an AppleID is to respond to the verification email sent to the email being used for the AppleID.

If you have an Apple mobile device you can also erase it and set it up as a new device. When doing so you have the option of not using a current email address and instead making an AppleID using an iCloud email address (so the process creates both an AppleID and a new iCloud account and thus uses the @icloud.com address created during that process).

See -> How to create a new Apple ID - Apple Support

MariposaTowers wrote:

Is it mandatory to use an email address as an apple ID? I cannot use my current one and I do not want to establish another email address just for this purpose. thank you

Yes. Apple IDs must be an email address.

You can get a free one from any number of providers in just a few minutes. Things like Outlook.com, Gmail, Yahoo.com and several others.