The Croatian would solve the Hammers full-back shortage.
The club have been searching for a replacement for Sam Allardyce since they parted ways after the final game of the season.
Bilic, himself a former West Ham player, will now be expected to add some of his trademark spice and style to proceedings at Upton Park.
One way he is being linked to do just that is by bringing in countryman from Croatia. Bilic is of course the former Croatia under-21 and senior manager, so knows plenty of talented Croats.
Two have already been linked, with Alen Halilovic of Barcelona B and Liverpool's struggling defender Dejan Lovren mentioned.
But the player they should be looking at is Sassuolo full-back Sime Vrsaljko.
The defender can play at left or right back and can also fill in on the wing. West Ham have recently lost Carl Jenkinson after his loan spell ended and were already short in this area. Vrsaljko can cover both positions.
Vrsaljko, who the Daily Mail linked with Watford in April, would be the perfect utility man for West Ham and given his links to Bilic would be easy to persuade.