Studying the star forming activity around type 1 Active Galactic Nuclei (AGN) has proven difficult due to the bright nucleus of AGNs outshines the classical starburst indicators, especially at optical and near-infrared spectral range. The mid-infrared IRS/Spitzer spectrum of several Palomar Green Quasi Stellar Objects (QSOs) have revealed the presence of Polycyclic Aromatic Hydrocarbons (PAHs) features in the nuclear spectrum, suggesting that starburst are present in most QSOs at kpc scales (~3 -21 kpc) from the nucleus.  We use the high angular resolution spectrum at N-band (~7.5-12 um) obtained with 10.4m Gran Telescopio CANARIAS to study the inner (< 1 kpc) star formation activity in a sample of local (z < 0.1) and MIR-bright (f_N > 0.02 Jy) QSOs. We measure the PAH at 11.3 um and calculate the inner star formation rate (SFR) at scales of few hundred pc (~300-1000 pc). The PAH is clearly detected in the 38 per cent of the sample, while an upper limit is reported for the rest. Using the same PAH and technique we measure the SFR at scales of few kpc using the IRS/Spitzer spectrum of objects in our sample. Comparing the inner and larger (Spitzer) aperture SFRs we conclude that star formation activity in QSOs is mostly concentrated within ~1 kpc. Finally, we find that our estimation of the SFR at scale of ~1kpc correlate with the black hole accretion rate as predicted by merger galaxy simulations at similar scales.