  Let $c$ be fixed with $1<c<35/34$. In this paper we prove that for every
sufficiently large real number $N$ and a small constant $\varepsilon>0$, the
diophantine inequality \begin{equation*} |p_1^c+p_2^c+p_3^c-N|<\varepsilon
\end{equation*} is solvable in primes $p_1,\,p_2,\,p_3$ near to squares.
