The rules are strict on this and the answer in most cases is no, at least not through the standard visitor approval process.
Correctional facilities run every visitor applicant through a background check that flags prior felony convictions. A former inmate with a felony record will be denied through the standard approval process regardless of the relationship to the person inside. That is the baseline rule across virtually every state and federal system.
The exception that sometimes exists is for family members. If you are related to the inmate and your conviction was completely unrelated to the crime that put them inside, there is a narrow path available through the warden's office. A special visitation waiver can be requested, and the warden has sole discretion to grant or deny it. Being a family member with no connection to the current offense is the strongest argument available for that waiver.
For friends rather than family, the path is considerably harder. A warden granting a visitation waiver to a former inmate who is not related to the person inside is uncommon. It happens but it requires an exceptionally compelling case made as respectfully and humbly as possible.
If you want to pursue it, write directly to the warden's office. Explain your relationship, your conviction and when it occurred, how your life has been conducted since release, and why maintaining this connection is a positive force for the inmate's rehabilitation and reentry. Keep the tone cooperative and do not make demands.
In the meantime, letters through InmateAid are available to anyone regardless of their own record. Writing is the most accessible way to stay connected while the visitation question works itself out.