Consider sets $A_0,A_1,\dots A_6$. 

Let $A_i=\{x : x\in \mathbb{N},\space 1\leq x\leq 2023, x\equiv i \text{(mod 7)}\}$

Each set has $\frac{2023}{7}=289$ elements.

Form pairs $(x,y)$ such that

$x\in A_1, y\in A_6$

$x\in A_2, y\in A_5$

$x\in A_3, y\in A_4$

As each set has $289$ elements, we can form $289$ pairs from each pair of sets. So, we can form $3\cdot 289=867$ pairs.