Sullivan frequently engages with Hammers fans on social networking site Twitter to give updates from behind the scenes.
With the January transfer window open, speculation is rife about players Slaven Bilic could be signing with reports the Hammers are in for the likes of Besiktas star Gokhan Tore (as reported by The Sun) and Leeds United's Sam Byram - as reported by the likes of the Metro.
Sell to buy
But Sullivan junior has taken to Twitter to update fans on the club's current transfer status and hopes for the future.
"All our wage cap is spent, so unless somebody goes we have no wages to pay them under PL rules," Sullivan posted.
NEWS : All our wage Cap is spent, so unless somebody goes we have no wages to pay them under PL rules.— Jack Sullivan (@jsullivanwhu) January 4, 2016
Strong push still expected in summer
That does not mean the Hammers won't be spending big in the summer, though.
With the club leaving their Boleyn Ground home of 112 years for the 54,000 seater Olympic Stadium many have tipped West Ham to start challenging the big guns on and off the pitch.
And Sullivan has added to the excitement, telling fans not to read too much into a lack of activity in the winter window.
@_AaronD7 no in the summer it's different! We are hoping to have a big summer window!!— Jack Sullivan (@jsullivanwhu) January 4, 2016
He added: "In the summer it's different! We are hoping to have a big summer window!"
Owners have given Bilic their backing
The Hammers were one of the busiest clubs in the last transfer window signing 12 players in total with a net spend of around £25-30 million including loan fees.
The east Londoners are widely considered to have done some of the best business of the summer overall.
Left-back Stephen Hendrie, goalkeeper Darren Randolph midfielders Pedro Obiang, Martin Samuelsen, Manuel Lanzini and Dimitri Payet and defensive reinforcements Angelo Ogbonna and Carl Jenkinson were all recruited over the summer.
That was before a quite memorable deadline day in east London where no less than a further four players were brought in.
Hull City striker Nikica Jelavic, Barcelona midfielder Alex Song, Chelsea star Victor Moses and Nottingham Forest's exciting and powerful winger Michail Antonio all signed up as the deadline day headlines were dominated by the Hammers.
With one of the strongest squads the club has had in decades and the Financial Fair Play limit reached it will take the sale of fringe players to free up some space on the wage bill if anyone is going to join Bilic's side this month.