  We state and prove the $q$-extension of a result due to Johnston and Jordaan
(cf. \cite{Johnston-2015}) and make use of this result, the orthogonality of
$q$-Laguerre, little $q$-Jacobi, $q$-Meixner and Al-Salam-Carlitz I polynomials
as well as contiguous relations satisfied by the polynomials, to establish the
quasi-orthogonality of certain $_2\phi_2$ and $_3\phi_2$ polynomials. The
location and interlacing properties of the real zeros of these quasi-orthogonal
polynomials are studied. Interlacing properties of the zeros of $q$-Laguerre
quasi-orthogonal polynomials $L_n^{(\delta)}(z;q)$ when $-2<\delta<-1$ with
those of $L_{n-1}^{(\delta+1)}(z;q)$ and $L_n^{(\delta+1)}(z;q)$ are also
considered.
