There is no relation (or only a very distant one).
A hardware interface attaches a network to a host (or devices like switches or router).
A port number in a transport-layer protocol (L4) serves as a subaddress on a host - that way, you can run multiple, independent applications on a host. Each subaddress/port allows you to address an application/a process on a host instead of the host as a whole (roughly). Without L4 ports, you couldn't run FTP, HTTP, SSH, SMTP, ... all on a single server.
From the network theory perspective, a hardware interface (physical layer L1) is multiplexed by using e.g. MAC addresses and VLANs in the data link layer (L2). That in turn is multiplexed by using e.g. IP addresses in the network layer (L3). That in turn is multiplexed using transport-layer protocols like TCP or UDP (L4). Many of those are then multiplexed using port numbers.