Slaven Bilic has some room for manouevre in his squad this month with Mauro Zarate having left for Fiorentina and Nikica Jelavic on his way to China.
Matt Jarvis' loan to Norwich City was made permanent at the beginning of the month while Arsenal loan defender Carl Jenkinson has returned to his parent club after picking up a season-ending injury.
Sam Byram has come in this January from Leeds United and Bilic is close to completing a move for Nigerian Emmanuel Emenike, as reported by the likes of the Evening Standard.
One of those targets is believed to be Marseille star Michy Batshuayi who the club hope to reunite with his former teammate Dimitri Payet.
But they will face stiff competition for the striker come the summer.
Hammers could adjust transfer plans
The 22-year-old is set to be the subject of a deadline day tug of war between Spurs and the Magpies and will not be allowed to leave the Hawthorns for anything less than £25 million, as reported by the Daily Mail.
That is the kind of money West Ham will be looking to splash out on a striker so Sullivan may feel he has no choice but to move for the England youth international, with the added incentive of beating bitter rivals Spurs of the punch.
Berahino scored both goals as West Brom were held to a 2-2 draw in the FA Cup against Peterborough on Saturday.