Does the double integral of ln(1 - xy)/(1 - xy) over [0,1]x[0,1] have a known closed-form?

I was looking at this double integral:

∬ over [0,1]×[0,1] of ln(1 - xy)/(1 - xy) dx dy

It looks simple in structure continuous over the unit square and reminiscent of integrals that collapse to zeta values.

But I couldn’t find any reference to a known closed-form.

Is this integral known to evaluate to a specific constant (e.g., involving pi or zeta values)? If yes, what are the techniques typically used to evaluate such integrals?

Any direction or insight would be appreciated.