Context. Recent studies have proposed that General Relativity Analysis via VLT InTerferometrY upgrade (GRAVITY+) on board the Very Large Telescope Interferometer (VLTI) is able to trace the circular orbit of the subparsec ( 0.1 pc) close-binary supermassive black holes (CB-SMBHs) by measuring the photo-centre variation of the hot dust emission. However, the CB-SMBHs orbit may become highly eccentric throughout the evolution of these objects, and the orbital period may be far longer than the observational time baseline. Aims. We investigate the problem of detecting the CB-SMBH with hot dust emission and high eccentricity (eCB-SMBH, e = 0.5) when the observed time baselines of their astrometric data and radial velocities are considerably shorter than the orbital period. Methods. The parameter space of the Keplerian model of the eCB-SMBH is large for exploratory purposes. We therefore applied the Bayesian method to fit orbital elements of the eCB-SMBH to combine radial velocity and astrometric data covering a small fraction of the orbital period. Results. We estimate that a number of potential eCB-SMBH systems within reach of GRAVITY+ will be similar to the number of planned circular targets. We show that using observational time baselines that cover 10% of the orbit increases the possibility of determining the period, eccentricity, and total mass of an eCB-SMBH. When the observational time baseline becomes too short (∼5%), the quality of the retrieved eCB-SMBH parameters degrades. We also illustrate how interferometry may be used to estimate the photo-centre at the eCB-SMBH emission line, which could be relevant for GRAVITY+ successors. Even if the astrometric signal for eCB-SMBH systems is reduced by a factor of √ 1 − e 2 compared to circular ones, we find that the hot dust emission of eCB-SMBHs can be traced by GRAVITY+ at the elementary level.