Nevertheless, West Ham hope Bilic's budding relationship with Conte can put them ahead of other clubs if the pair become available.
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GETTY
Slaven Bilic and Antonio Conte during last month's EFL Cup tie
West Ham are also said to be keeping an eye on Daniel Sturridge's situation at Liverpool.
The England striker is unhappy with being on the bench under Jurgen Klopp and reportedly wants to leave.
However his £150,000-a-week wages could scupper any move to the London Stadium.