The Hammers are chasing a top four finish in the Premier League this season and boss David Moyes is eyeing at bolstering his squad in the upcoming window.
Revamping their defence is a priority for West Ham in January, but they will also look to make attacking additions as they look to support their existing options.
The capital club are evaluating potential targets ahead of the winter window and Verona attacking midfielder Barak is among the names in their sights.
It is claimed they are hugely keen on the 27-year-old, but face an obstacle in the shape of Verona.
Verona are firmly opposed to selling the player in January and will only reconsider if a large offer is made.
Barak, a Czech Republic international, has shared the international stage with Hammers duo Tomas Soucek and Vladimir Coufal.
Both Coufal and Soucek have become key players under Moyes since arriving at the London Stadium and it remains to be seen whether West Ham will try to add to their Czech Republic contingent by bringing in Barak next month.
