It comes after Slaven Bilic was left without key strikers Diafra Sakho and Andy Carroll for much of the season due to injury.
While Carroll's injury problems are well documented, Sakho has also spent a lot of time in the treatment room since his move from Metz in the summer of 2014.
With that in mind Sullivan hopes to bring in a mystery striker and did not want to give too much away, telling Sky Sports: "He is an overseas striker. If I told you (the league) you wouldn’t believe (it)."
That cryptic message has sent social media and West Ham forums into meltdown with speculation over who it might be with two of the contenders familiar names to most Hammers fans.
West Ham summer target and France striker Andre-Pierre Gignac, a former teammate of new Hammers hero Dimitri Payet at Marseille.
Gignac was heavily linked with a move to East London and a number of European clubs in the summer, as reported by the likes of the Metro, but instead made something of a shock move to Mexican side Tigres UANL instead.
The 30-year-old has proved his class in South America scoring 16 goals in his first 22 games for Tigres.
Deadly partnership with Payet
He formed a deadly partnership with Payet at Marseille with the pair combining to score 74 goals in 226 games and making countless more.
Gignac is said to be desperate to come back to Europe in a bid to force his way back into the French squad as they prepare to host this summer's European Championships.
The other name being heavily linked is former Hammers striker Demba Ba.
Ba scored seven goals in 12 games for the Hammers but could not help them avoid relegation under the hapless Avram Grant back in 2011.
It is not only West Ham's board and fans Ba is well known to, though.
The 30-year-old Senegal star was signed by Bilic for Besiktas in 2014 after a frustrating year on the bench at Chelsea.
He went on to maintain his formidable career average of a goal every other game - he has 134 goals in 274 club matches - and scored 18 goals in 29 games for Besiktas under Bilic.
Ba, currently plying his trade for Shanghai Shenhua in China, was the first person to wish his old boss well when he landed the West Ham job last summer and could be reunited with his old boss at his old club this window.
The youngest of the trio at 28, Nigerian striker Emenike is the hot favourite to be the mystery player Sullivan has alluded to.
Emenike, who likes to wear the number 99, has 80 goals in 186 games in his career so far.
It is a career which has seen him come up against Bilic on numerous occasions, first when the former Croatia boss was in charge of Lokomotiv Moscow while Emenike was at their bitter rivals Spartak.
Then during the striker's time at Fenerbace, rivals to Bilic's Besiktas, where the African scored 16 goals in 55 appearances.
He was loaned to the most successful club in the footballing backwater that is the UAE League this season when he joined Al Ain FC.
Hammers fans should remember one of their best players this season also arrived on loan from that league this year in the shape of Manuel Lanzini.
Emineke has nine goals in 15 games for AL Ain, the same number of goals he has for Nigeria from 39 caps for his country.