David Moyes wants more options who can play on the left in his side and West Ham have been tracking several different players who could do a job.
Kostic was part of the Eintracht Frankfurt side that won the Europa League last season, where they did beat West Ham in the semi-final over two legs, and caught the eye with his displays.
West Ham have laid their eyes on the Serbian and are now pushing to take him to the London Stadium.
It has been claimed that the Hammers have put in an official bid with Eintracht Frankfurt for the midfielder’s signature.
The 29-year-old has a year left on his contract and Eintracht Frankfurt are prepared to sell him this summer.
Several clubs across Europe have been tracking Kostic this summer but West Ham have now made a concrete move.
The figures of the potential deal are yet to filter through but the Hammers are making a play to land Kostic.
They are hoping to work out an agreement with Eintracht Frankfurt before trying to convince Kostic to move to the London Stadium.