Suppose that it came to my attention someone had stolen from my company, or committed some other crime that only hurts my company. Is it legal for me to send a letter asking for compensation in return of not suing nor pressing charges?
Is it legal for me to send a letter asking for compensation in return of not suing nor pressing charges?
Yes, provided that by compensation you mean the equivalent (or close thereto) of what he stole. Your mention that the letter is on behalf of the company is crucial.
Although definitions of extortion make reference to "[acting] under color of office", U.S. v. Harris, 916 F.3d 948, 955-956 (2019) notes that states as well as Congress adopted an extended definition so as to include [extortion by] private individuals.
One incurs extortion also when seeking to obtain more than is due. See, for instance Black's Law Dictionary (4th edition) just prior to the entry for "Extortion". Thus, a surcharge on administrative grounds would be reasonable, but the company ought to ensure that the surcharge does not land it in the "more than is due" zone. The same applies in the event that stealing the property caused provable losses. See also conversion.