Context : The launch of the Fermi Gamma-ray Space Telescope  in 2008 opened new perspectives in the multi-wavelength studies of neutron stars , with more than 100 \gamma -ray pulsars now detected . While most Fermi  pulsars have been already observed in the X-rays with Chandra  and XMM-Newton , optical observations with 8m-class telescopes only exist for a tiny fraction of them . Aims : Here , we aim at searching for optical emission from the Fermi  pulsar PSR J1028 - 5819 ( P = 91.4 ms ) . With a spin-down age \tau = 92.1 kyr and a rotational energy loss rate \dot { E } \sim 8.43 \times 10 ^ { 35 } erg s ^ { -1 } , PSR J1028 - 5819 can be considered a transition object between the young , Vela-like pulsars and the middle-aged ones . At a distance of \sim 2.3 kpc and with a relatively low hydrogen column density , PSR J1028 - 5819 is a good potential target for 8m-class telescopes . Methods : Due to its recent discovery , no optical observations of this pulsar have been reported so far . We used optical images taken with the Very Large Telescope  ( VLT ) in the B and V bands to search for the optical counterpart of PSR J1028 - 5819 or constrain its optical brightness . At the same time , we used an archival Suzaku  observation to confirm the preliminary identification of the pulsar ’ s X-ray counterpart obtained by Swift . Results : Due to the large uncertainty on the pulsar ’ s radio position and the presence of a bright ( V = 13.2 ) early F-type star at \la 4 \arcsec ( Star A ) , we could not detect its counterpart down to flux limits of B \sim 25.4 and V \sim 25.3 , the deepest obtained so far for PSR J1028 - 5819 . From the Suzaku  observations , we found that the X-ray spectrum of the pulsar ’ s candidate counterpart is best-fit by a power-law with spectral index \Gamma _ { X } = 1.7 \pm 0.2 and an absorption column density N _ { \mathrm { H } } < 10 ^ { 21 } cm ^ { -2 } , which would support the proposed X-ray identification . Moreover , we found possible evidence for the presence of diffuse emission around the pulsar . If real , and associated with a pulsar wind nebula ( PWN ) , its surface brightness and angular extent would be compatible with the expectations for a \sim 100 kyr old pulsar at the PSR J1028 - 5819 distance . Conclusions : A far more accurate radio position for PSR J1028 - 5819 is necessary to better determine its position relative to Star A . Future high-spatial resolution observations with both the HST  and Chandra  are better suited to disentangle the optical emission of PSR J1028 - 5819 against the halo of Star A and to confirm the existence of the candidate PWN .