Moyes, who has been out of work since resigning from Sunderland in May after their top-flight relegation, denied there had been contact, but made it clear he wanted to return to club management.
"I've always said I want to go back into club management. If the right opportunity comes around, I'll be interested," the 54-year-old Scot told Bein Sports.
When asked if he could take the West Ham job, Moyes replied: "I am interested but at the moment that vacancy has not become available."
The former Everton manager's stock has fallen considerably in recent years, following an unsuccessful spell at Spanish side Real Sociedad and an ill-fated spell as Alex Ferguson's successor at Manchester United in 2013-14.
"I've been there myself what Slaven is going through at the moment and he must be hating it and wanting to get a result as quickly as he can," he added.
Bilic's West Ham have won just two league games this season and have lost three of last four matches at the London Stadium.
Their 4-1 defeat by Liverpool on Saturday left them 18th and in the relegation zone with nine points from 11 games.
(Reporting by Hardik Vyas in Bengaluru; editing by Amlan Chakraborty)
