There are many, many ways to avoid personal pronouns. One is the passive voice, but often there are simply alternative ways of phrasing.
Thank you, #PERSONNAME for contacting me.
- Thank you, #PERSONNAME, for your enquiry.
- Thank you, #PERSONNAME, for getting in touch.
- Thank you, #PERSONNAME, for considering this firm/company/business
I don't know of anyone at the moment who meets your needs
- There is nobody on our books who currently meets your needs
- None of the current list of job-seekers quite fit the bill
but my contacts may be able to suggest someone who does
- but enquiries may well turn up a good match
if I find someone interested in the position I will let you know about it
- You can expect to hear (from us) as soon as a suitable candidate is found.
- ... who will promptly be passed on to you.
Since you (or the person saying I, if that is not you) represent a business, one simple way to reduce repetition is to switch between I/my/me and we/our/us. Another, as I have shown, is to refer to the company or to shift the subject to another person/people in the sentence ("There is nobody" rather than "I don't know of anybody"). Switching between several of these different options, while still occasionally saying I, will be better than simply alternating between I and we (which would risk looking artificial and strained).