Yes, you can say ‘I look forward to hearing from you’ in your cover letter. Employers expect to see a call-to-action like this at the end of your cover letter, as it demonstrates your genuine interest in the role.
But if you want to avoid using this common phrase, here are some alternatives:
I’m excited to hear back from you soon
Awaiting your kind response at your earliest convenience
Anticipating your reply
And remember to include your email address and phone number when you use this phrase. Even though this information should be in your cover letter header, repeating it in your closing paragraph ensures it’s easy for the employer to find.