  Combination of advanced high power laser technology, new acceleration methods
and achievements in undulator development opens a way to build compact, high
brilliance Free Electron Laser (FEL) driven by a laser wakefield accelerator
(LWFA). Here we present a study outlining main requirements on the LWFA based
Extreme Ultra Violet (EUV) FEL setup with the aim to reach saturation of photon
pulse energy in a single unit commercially available undulator with the
deflection parameter $K_0$ in a range of (1{\div}1.5). A dedicated electron
beam transport which allows to control the electron beam slice parameters,
including collective effects, required by the self-amplified spontaneous
emission (SASE) FEL regime is proposed. Finally, a set of coherent photon
radiation parameters achievable in the undulator section utilizing best
experimentally demonstrated electron beam parameters are analyzed. As a result
we demonstrate that the ultra-short (few fs level) pulse of the photon
radiation with the wavelength in the EUV range can be obtained with the peak
brilliance of $\sim$2$\times$10$^{30}$ photons/s/mm$^2$/mrad$^2$/0.1%bw if the
driver laser operates at the repetition rate of 25 Hz.
