Oyarzabal has scored six goals in eight La Liga appearances for Real Sociedad this season and has even earned an international call up from Spain.
The 20-year-old is on course to become one of his country's next big stars, but could West Ham hold an ace in the pack among chasing clubs?
Oyarzabal's success is partly thanks to new Hammers boss David Moyes.
Moyes spell in Spain in charge of Real Sociedad is largely written off as a failure, but there were a couple of bright moments.
One was a famous win over Barcelona, his other big claim is that he was the manager to hand Mikel Oyarzabal his debut.
Moyes brought him into his pre-season squad and picked him for the first time in the October of the 2015/16 season, and Oyarzabal has not looked back since.
Moyes was sacked just one month later, but his faith in Oyarzabal set the young talent en route to his success.
Now he is wanted by many of Europe's top clubs, and this includes Tottenham, who knocked off Real Madrid last month.
Moyes could try to convince Oyarzabal that West Ham are the right level of club for the winger to move to at this stage of his career, and has a personal connection to the player.
If the Scotsman could pull it off - and he may need to sell to buy in order to - it would be one of the coups of the season.