Tottenham Hotspur have been linked with the 23-year-old, but should another London club throw their hat into the ring?
It is no secret that West Ham United's Robert Snodgrass has proved an inadequate replacement for Dimitri Payet, having scored none and set up two Premier League goals since a £10 million switch to East London from Hull City in January.
West Ham boss Slaven Bilic certainly needs a big upgrade on the Scotland international - and Kovacic is perfect.
The Croatia international could be the creative spark that the Irons have desperately lacked since Payet re-joined Marseille and, at 23, he is only going to get better - a lot better.
The Daily Star reported at the weekend that Kovacic be sold for just £22 million - a bargain in the modern climate of huge transfer fees - and if Tottenham sign him for that figure and he ends up being a hit, West Ham can only blame themselves.
The Irons need him more than Tottenham, who have Dele Alli and could possibly even have Ross Barkley by September, and failing to try would be unacceptable.
Snodgrass, at £10 million, was a mistake, but Bilic can and should make it better with a swoop for Kovacic.