I don't know whether it's "normal" or not, but I went 90% of the way to Crazyville with my DD1 who was compulsively verbal. In fact, if she didnt have anything to say, she would repeat things & even make random noises.

I have in more recent times wondered whether this wasn't part of a sensory issue, like a stimming behaviour.

Some of the strategies we used
* insert music - it gets them listening differently. Sometimes I would even sing the thing I wanted to say
* give her other types of noisy play - eg drums, percussion instruments, keyboard. Rule was she had to play them in her room or outside
* teaching that there are speech cues - like checking first that someone is looking at you before you talk. Phrases like "look at me" and "watch my face" can help with checking that people are listening
* take a break - build more kid-free mummy time into your routine & get more sleep so you've got more in your tank to cope with it, because it can be quite stressful being bombarded with all that chatter.

Good luck, it will pass eventually & it will be a joy to have a DD who always wants to chat to her mum.