Dragovic has impressed for the Ukrainian outfit all season and he looks to be one of the most exciting defenders across Europe.
Although he would not come cheap, West Ham are said to feel he could enhance the quality of their squad considerably and they could make a move to sign him this summer.
The 24-year-old possesses a commanding presence in the air and if West Ham did manage to capture him it would be a real statement of their intent to challenge for high positions in the Premier League.
Impact for West Ham?
The Hammers' need for a centre-back was reduced by Winston Reid's decision to sign a new centre-back, but they could still be looking for further additions.
West Ham have recently expressed their desire to be challenging for the Champions League and if they do want to make it into the top-four than they will need to add numbers to their squad.
Sam Allardyce's men have suffered this season due to a lack of quality cover and they are clearly hoping to bolster their options in the summer transfer window to ensure that their season doesn't peter out again.
At the moment there is a suggestion that Dragovic's reported £15 million price-tag is out of the Hammers' price range, but if David Sullivan and David Gold are going to backup their ambitious statements then they will have to open up their cheque books to land players of the quality required.