ABSTRACT In a previous paper, we reported evidence for quasi-periodicities in the Transiting Exoplanet Survey Satellite (TESS) light curves of BL Lacerate and two other blazars found serendipitously in the Sloan Digital Sky Survey (SDSS) active galactic nuclei catalogue. In this work, we find tentative evidence for quasi-periodic features in the TESS observations of five sources in the fourth catalogue of the Fermi–Large Area Telescope sources: J090453.4−573503, J2345−1555, B0422+004, J002159.2−514028, and B0537−441. We analysed the TESS light curves of these blazars that we extracted using a customized approach. The quasi-periodic oscillations (QPOs) are searched for using two timing analysis techniques: generalized Lomb–Scargle periodogram and weighted wavelet Z-transform. Their apparent periods lie in the range of 2.8–6.5 d and have at least 3σ significance in both of these methods. QPOs at such time-scales can originate from the kink instability model which relates the quasi-periodic feature with the growth of kinks in the magnetized relativistic jets. We performed Markov Chain Monte Carlo simulations to obtain the posterior distribution of parameters associated with this model and found the kink period consistent with previous studies.