Besiktas coach Bilic is fondly remembered at Upton Park after impressing as a defender during his playing days between 1996 and 1997.
Allardyce's future at the Premier League club has been shrouded in doubt after a promising opening half to the season has been followed by a dismal run of form in 2015, with the club winning just two league matches since the turn of the year.
Former Croatia boss Bilic has been linked with a return to the club, but he insists there is no substance in the reports.
In an interview with Fanatik, Bilic said: "I do not know who keeps spreading the West Ham link but I can tell you I am not in talks with the club.
"My future will be decided at the end of the season with Besiktas.
"I am very pleased with the work I do, and think I do my job well. I have not received an offer from anyone."
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