The Hammers are expected to be active in this month's transfer market with a forward believed to be top of Bilic's wishlist following the decision to cut Simone Zaza's loan spell short.
With the Italian having returned to Juventus, and with Diafra Sakho currently injured, Bilic is short of strikers and reportedly tabled a £6million to sign Sunderland striker Defoe on Wednesday.
That offer was rejected by the Black Cats but West Ham are said to be maintaining their interest and are thought to be willing to up their offer.
Bilic says he is a fan of the former Hammers youngster and admits the club are working on adding to their squad in January, but refused to confirm whether Defoe is one of their targets.
"We are not going to discuss the players that are not ours at the moment," Bilic said. "The chairman is trying really hard to get some players, in a position that we need. But I am not going to talk about names here in public."
On Defoe, Bilic said: "I said last time that he does the things that are the most important in football; score goals.
"He did that last year and he was probably the main reason Sunderland stayed up. He is doing it again this season, but he is also making chances and making them into goals."
West Ham have also been linked with a move for Brentford striker Scott Hogan, reportedly having a £10million bid rejected, and Bilic feels the 24-year-old is an exciting prospect.
"He is, again, scoring goals. He is very sharp, quick. A good finisher - doing it in the Championship, young and a good prospect," he added.