  Given $\epsilon>0$, we show that over an algebraically closed field of
characteristic $p>5$, the anticanonical volume of a Fano threefold $X$ (with
arbitrary singularities) whose anticanonical divisor has Seshadri constant
$\epsilon(-K_X,x)>2+\epsilon$ at some smooth point $x\in X$ is bounded from
above.
