Interface transfer operators (IT) provide boundary conditions between multiphysics problems coupled over an interface, which are ubiquitous in science and engineering application. ITOs derived from hybrid-monolithic mathematical formulations such as Lagrange multiplier-based (LM) coupling approaches have been shown to have improved stability and accuracy properties when compared to those used in many partitioned coupling schemes. The disadvantage to such methods is their increased level of intrusiveness. That is, the interface operator that must be formed to solve for the coupling traction forces requires access to other subdomain operators, which are generally embedded deeply within the software modeling the subdomains physics. We present an approach for data-driven discovery of the interface transfer operator. With this approach, we are able to loosen the requirements for access to multiple complex subdomain data structures. The resulting coupling operators are relatively nonintrusive to form, are amenable to tuneable fidelity, and are less computationally expensive to evaluate than the full-order coupling operator. With the rise in popularity of data-driven modeling techniques applied to subdomain problems, we make the assumption of the availability of full-resolution subdomain solution data on at least one subdomain and then leverage an idea by Carey et. al. [1] from which to generate high-order approximations of traction forces for snapshots. We use the traction force snapshots to generate a reduced basis and then perform ordinary least squares operator regression to approximate the Schur complement system. The approach is minimally burdensome, requiring only Gramian matrices capturing a surface integral of solution trial and LM test functions over the interface. We demonstrate the effectiveness of the technique with several numerical experiments and make comparison with respect to speed against Schwarz-based approaches and a full-order, Schur complement-based approach. [1] G. Carey, S. Chow, M. Seager, Approximate boundary-flux calculations, Computer Methods in Applied Mechanics and Engineering 50 (2) (1985) 107 – 120. doi:http://dx.doi.org/10.1016/0045-7825(85)90085-4.