The gluon-gluon fusion for $\eta_c$ and $\chi_c$ quarkonium production
is known to be the dominant mechanism [1,2]. In contrast the mechanism of light $f_2(1270)$ tensor meson production is not known. We calculate inclusive cross section for $f_2(1270)$ tensor meson production for gluon-gluon fusion in the $k_t$-factorization approach using different unintegrated gluon distributions from the literature . The process is also interesting in the context of searches for saturation effects encoded in unintegrated gluon distributions. The energy-momentum tensor, equivalent to $L=2$, $J_z = 2$ and $L=2$ , $J_z = 0$ couplings are used for the $g^* g^* \to f_2(1270)$ vertieces. The parameters are extracted from $\gamma \gamma \to f_2(1270) \to \pi \pi$ reactions by comparison to Belle data on $\gamma \gamma \to \pi^+ \pi^-$ and $\gamma \gamma \to \pi^0 \pi^0$ reactions. The results strongly depend on the parametrization of the $g^* g^* \to f_2(1270)$ form factor. Our results for $p p \to f_2(1270)$ are compared to preliminary ALICE data. The agreement with the data can be achieved only at larger $f_2(1270)$ transverse momentum, only for some parametrizations of the $g^* g^* \to f_2(1270)$ form factor. No obvious sign of the onset of saturation is observed. At low transverse momenta one needs to include also final state pion-pion rescattering. The agreement with the ALICE data can be obtained by adjusting probability of formation and survival of $f_2(1270)$ in a harsh quark-gluon and multipion enviroment.
 I. Babiarz, R. Pasechnik, W. Schaefer and A. Szczurek, JHEP2002, 037 (2020).
 I. Babiarz, R. Pasechnik, W. Schaefer and A. Szczurek, paper ready for submission.
 P. Lebiedowicz and A. Szczurek, a paper in preparation.