The Hammers were one of the busiest clubs over the summer bringing in former Croatia boss Bilic to replace Sam Allardyce and bolstering his squad with 12 new players.
Bilic's first signing was Spanish midfielder Pedro Obiang, who has been impressive each time he has played for his new club since signing from Serie A side Sampdoria.
The 23-year-old signed the day after Bilic joined the club back in June, prompting questions over who had targeted the Spain Under 21 international.
At the time Bilic told the club's official website he had monitored the player and spoken to a number of contacts based in Italy.
Talent spotter gets credit
But now in an interview with the Mirror, Sullivan has revealed Bilic had nothing to do with the Obiang deal, saying the midfielder was targeted and signed by the club's talent spotter Tony Henry.
“Tony brought in Obiang," Sullivan told the Mirror.
"He cost £4.5m. I think he is going to turn out to be a good player."
Reason behind lack of game time?
Despite impressing when he has played with his vision and incisive passing in that Michael Carrick-esque role, Obiang has found game time hard to come by in recent weeks.
After suffering an injury early on, Obiang has only featured in six of the Hammers' 15 competitive games so far this season - including the Europa League qualifiers.
Many Hammers fans feel he should be in Bilic's starting line-up each week particularly given the indifferent form of captain Mark Noble, who was substituted an hour into Saturday's win over Crystal Palace.
But he has been left kicking his heels in recent weeks.
While there is no suggestion Bilic is ignoring the player purely because he was signed by someone else, there is little doubt his loyalty would be with players like Noble – who he decided to make his captain – and Manuel Lanzini, who was a player he had been tracking for two years.
Do the fans really care?
Much is made of managers not controlling transfer targets in this country.
But the truth is West Ham fans won't care who is responsible while the team continues to get results and signings keep impressing as they have done.
While the Hammers have the combative qualities of Noble, the attacking brilliance of Dimitri Payet and the endless stamina and quality of Cheikhou Kouyate in the centre of the park, Obiang offers the ability to not only to break up play, but also to use his passing to open up teams on the counter attack.
The trouble is if Obiang is struggling to get games now, it will be even more difficult when Alex Song, a player Bilic said he was desperate to sign, returns to first team action in the next few weeks.