Experimental studies have shown that in cortical neurons, excitatory and inhibitory incoming currents are strongly correlated, which is hypothesized to be essential for efficient computations. Additionally, cortical neurons exhibit strong preference to particular stimuli, which combined with the co-variability of excitatory and inhibitory inputs indicates a detailed co-tuning of the corresponding populations. Such co-tuning is hypothesized to emerge during development in a self-organized manner. Indeed, theoretical studies have demonstrated that a combination of plasticity rules could lead to the emergence of E/I co-tuning in neurons driven by low noise signals from feedforward connections. However, cortical signals are very noisy and originate in highly recurrent networks, which raises a question on the ability of known plasticity mechanisms to self-organize co-tuned connectivity. We demonstrate that high noise levels combined with random recurrence destroy co-tuning. However, we demonstrate that introducing structure in the connectivity patterns of the recurrent E/ I network, the recurrence does not hinder but enhances the formation of the co-tuned selectivity. We employ a combination of analytical methods and simulation-based inference to uncover constraints on the recurrent connectivity that allow E/I co-tuning to emerge. We find that stronger excitatory connectivity within similarly tuned neurons, combined with more homogeneous inhibitory connectivity enhances the ability of plasticity to produce co-tuning in an upstream population. Our results suggest that structured recurrent connectivity controls information propagation and can enhance the ability of synaptic plasticity to learn input-output relationships in higher brain areas.