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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 polynomialsas well as contiguous relations satisfied by the polynomials, to establish thequasi-orthogonality of certain $_2\phi_2$ and $_3\phi_2$ polynomials. Thelocation and interlacing properties of the real zeros of these quasi-orthogonalpolynomials are studied. Interlacing properties of the zeros of $q$-Laguerrequasi-orthogonal polynomials $L_n^{(\delta)}(z;q)$ when $-2<\delta<-1$ withthose of $L_{n-1}^{(\delta+1)}(z;q)$ and $L_n^{(\delta+1)}(z;q)$ are alsoconsidered.

Quasi-orthogonality and zeros of some ${}_2\phi_2$ and ${}_3\phi_2$ polynomials