Context. Hot Jupiters (HJs) with close-by planetary companions are rare, with only a handful of them having been discovered so far. This could be due to their suggested dynamical histories, which lead to the possible ejection of other planets. TOI-2109 b is special in this regard because it is the HJ with the closest relative separation from its host star, being separated by less than 2.3 stellar radii. Unexpectedly, transit timing measurements from recently obtained CHEOPS observations show low-amplitude transit-timing variations (TTVs). Aims. We aim to search for signs of orbital decay and to characterise the apparent TTVs in an attempt to gain information about a possible companion. Methods. We fitted the newly obtained CHEOPS light curves using TLCM and extracted the resulting mid-transit timings. Successively, we used these measurements in combination with TESS and archival photometric data and radial velocity (RV) data to estimate the rate of tidal orbital decay of TOI-2109 b, and also to characterise the TTVs using the N-body code TRADES and the photo-dynamical approach of PyTTV. Results. We find tentative evidence at 3σ for orbital decay in the TOI-2109 system when we correct the mid-transit timings using the best-fitting sinusoidal model of the TTVs. We do not detect additional transits in the available photometric data, but find evidence supporting the authenticity of the apparent TTVs, indicating a close-by, outer companion with Pc > 1.125 d. Due to the fast rotation of the star, the new planetary candidate cannot be detected in the available RV measurements, and its parameters can only be loosely constrained by our joint TTV and RV modelling. Conclusions. TOI-2109 could join a small group of rare HJ systems that host close-by planetary companions, only one of which (WASP-47 b) has an outer companion. More high-precision photometric measurements are necessary to confirm the existence of this planetary companion. ★This study uses CHEOPS data obtained as part of the Guaranteed Time Observation (GTO) programmes CH_PR100012 and CH_PR140063.
