Let $X$ and $Y$ be normed spaces over a complete field $\Bbb{F}$ with dual spaces $X'$ and $Y'$ respectively. Under certain hypotheses, for given $x\in X$, $y\in Y$ and a mapping $u$ from $X'\times Y'$ to $\Bbb{F}$, we apply Hyers--Ulam approach to find a unique bounded bilinear mapping $v$ near to $u$ such that $||v||=||x\otimes y||$.