“Chelsea did everything they could do to try to sign John Stones in the summer but Everton refused to do business with them,” Bilic wrote in The London Evening Standard.
“That takes guts. We also had an interest in Kevin Mirallas but we were not able to get him.”
Mirallas has been on the books of Everton since 2012 and is one of the better wingers in the Premier League.
The Belgium international, though, has struggled to play regularly for the Toffees so far this season.
The former Olympiacos star has featured in only five Premier League matches this campaign, creating two chances in the process.
West Ham’s performances and results so far this season suggest that they are not missing Mirallas.
The Hammers are sixth in the Premier League table at the moment with 20 points from 11 matches, just a point behind fourth-place Manchester United.
The London outfit will take on Everton at the Boleyn Ground in the league on Saturday afternoon. The Toffees are currently ninth in the standings with 16 points from 11 matches.