talkSPORT understands that Fenerbahce centre-back Attila Szalai and Manchester United's Jesse Lingard are on David Moyes' radar.
Having had a fairly impressive season so far, the Hammers are now looking to add reinforcements as they continue to push for success in the Premier League, Europa League and FA Cup.
Given the injuries they have had this season in defence, such as to Angelo Ogbonna, it is understandable as to why Moyes wants more bodies in that position.
West Ham do, though, face competition for 23-year-old is fierce though as Newcastle United are also reportedly keen on him.
talkSPORT's football correspondent Alex Crook told White and Jordan: "They're in for the Hungarian international Attila Szalai, he was part of the team for last year's delayed European Championship.
"I think he played pretty much every minute, if not every minute, for Hungary. Plays his club football for Fenerbahce, would cost around £17million.
"He's been linked with Chelsea in the past by the Hungarian national team coach [Marco Rossi], I know for a fact West Ham have been tracking him since last summer."
Funds are not expected to be an issue for West Ham though following Czech billionaire, Daniel Kretinsky's minority purchase in the club.
As well as pushing for a deal for Szalai, Crook also revealed the Irons still want to bring in Lingard this month.
"They've not given up hope, I'm told, of prizing Jesse Lingard away from Manchester United," he added.
"So West Ham could be one of the busier clubs in the Premier League come the next couple of weeks."
The England international is expected to leave Old Trafford upon the expiration of his contract this summer having been frustrated with game time this season.
Similarly to Szalai, though, a deal for the 29-year-old may not be straightforward as Tottenham are also keen on him.
Spurs also want him now, but are happy to wait until the summer when they won't have to negotiate with Man United.
Lingard excelled in east London last season, scoring nine goals in 16 matches as the Hammers sealed qualification for the Europa League.