  We investigate $\Lambda\Lambda$ interaction dependence of the
$\Lambda\Lambda$ intensity correlation in high-energy heavy-ion collisions. By
analyzing the correlation data recently obtained by the STAR collaboration
based on theoretically proposed $\Lambda\Lambda$ interactions, we give a
constraint on the $\Lambda\Lambda$ scattering length, $-1.25~\text{fm} < a_0 <
0$, suggesting that $\Lambda\Lambda$ interaction is weakly attractive and there
is no loosely bound state. In addition to the fermionic quantum statistics and
the $\Lambda\Lambda$ interaction, effects of collective flow, feed-down from
$\Sigma^0$, and the residual source are also found to be important to
understand the data. We demonstrate that the correlation data favor negative
$\Lambda\Lambda$ scattering length with the pair purity parameter
$\lambda=(0.67)^2$ evaluated by using experimental data on the
$\Sigma^0/\Lambda$ ratio, while the positive scattering length could be favored
when we regard $\lambda$ as a free fitting parameter.
