Slaven Bilic turned down the chance to sign Renato Sanches and Grzegorz Krychowiak, according to David Sullivan.
Sanches joined Swansea City on loan in one of the shock deals of the summer, with Chelsea, Liverpool and Manchester United all credited with interest.
However, Sullivan claims that the former Benfica man could have been a Hammers player had Bilic given the green light.
“Grzegorz Krychowiak and Renato Sanches were both offered to the manager before their switches elsewhere, but he told us that he is happy with the squad he has,” Sullivan said.
“As a Board we are behind Slaven, and he believes he has the tools to turn around our form and rectify our disappointing start to the season.”
Pablo Zabaleta, Marko Arnautovic and Javier Hernandez all joined the Hammers in the summer, but they did miss out on William Carvalho after Sporting Libson left it too late to accept a club-record bid.
“Overall Slaven is happy with the business we have done during the summer transfer window,” said Sullivan. “We received the manager’s wish-list before the window opened and we have managed to get the top four players on it.
“It is no secret that we made a club record bid for Sporting Lisbon’s William Carvalho but unfortunately that offer was rejected a couple of weeks ago.
“Late last night Sporting Lisbon made contact to accept the original offer, but unfortunately it was just too late in the day, and we simply did not have enough time to put the player through a medical.
“We were not prepared, as a club, to buy a player for that amount of money without him having gone through adequate medical checks.”