There are lots of looking forward to questions, such as this one.
Can this sentence:
"I am looking forward to hearing from your reply"
Also be written as:
"I am looking forward to your reply"
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We use the second one:
I am looking forward to your reply.
We don't hear from the reply, we hear from you. What we hear from you is the reply.
Here are various options you can use (informal):
The following use 'I look' and are more formal versions of the above examples:
Note that 'hearing' can refer to written/read communication (letter, email or text). However, I avoid using 'hearing' to refer to emails. So when I submit a job application, I write 'I look forward to any communication from you ...'.
1. Credit to @user3724662, which is a very good answer.