The Hammers are hoping to boost their strength and depth in the squad and have targeted various options.
It looks like the Olympiakos man could be on his way to the club as West Ham’s second signing after the confirmed the arrival of Roberto as competition in goal.
West Ham had been pursuing other targets in central midfielder as well.
With just Declan Rice and Mark Noble staking a real claim for the positions, and arguably Robert Snodgrass, the Irons are in real need for midfield depth.
Last summer they did bring in Arsenal’s academy graduate Jack Wilshere, but as he so unfortunately has throughout his career, the English midfielder got injured and missed most of the season, as has fan favourite Manuel Lanzini.
This has led the club to pursue midfield targets, the most recent and high profile being Andre Gomes.
The Barcelona midfielder was on loan at Everton and shone on several occasions, showing his class and attracting reported interest from Tottenham Hotspur and Arsenal.
It is understood Everton want to bring him to the club permanently, but West Ham have made the first moves with an £18m bid.
Unfortunately for Manuel Pellegrini, West Ham’s bid was rejected, with Barcelona holding out for a reported £25-£35m.
It seems West Ham have now turned their attention to another target in the form of Fortounis, who only has one year left on his contract, according to the Sun.
The Greek midfielder has been highly recommended by sporting director Mario Husillos and is expected to be within the Hammers’ price range.
Husillos worked with Fortounis during a brief spell at Olympiakos, so has had the opportunity to evaluate the midfielder himself.
Other targets away from the Greek international and Barcelona’s Gomes include Villarreal’s Pablo Fornals.
There are also outgoings to keep an eye on at West Ham, with midfielder Edmilson Fernandes on the brink of join Mainz for £8m, so Pellegrini will most certainly need to bolster his midfield depth if West Ham are to kick on next season.