The optimization and scheduling of scientific observations done with instrumentation supported by adaptive optics could greatly benefit from the forecast of PSF figures of merit (FWHM, Strehl Ratio, Encircle Energy and contrast), that depend on the AO instrument, the scientific target and turbulence conditions during the observing night. In this contribution we explore the the possibility to forecast a few among the most useful PSF figures of merit (SR and FWHM). To achieve this goal, we use the optical turbulence forecasted by the mesoscale atmospheric model Astro-Meso-NH on a short timescale as an input for PSF simulation software developed and tailored for specific AO instruments. A preliminary validation will be performed by comparing the results with on-sky measured PSF figures of merit obtained on specific targets using the SCAO systems SOUL (FLAO upgrade) feeding the camera LUCI at LBT and SAXO, the extreme SCAO system feeding the high resolution SPHERE instrument at VLT. This study will pave the way to the implementation of an operational forecasts of such a figure of merits on the base of existing operational forecast system of the atmosphere (turbulence and atmospheric parameters). In this contribution we focus our attention on the forecast of the PSF on-axis.