The Mirror report that Fulham see Cole as a ready-made replacement for Bobby Zamora.
Birmingham boss Alex McLeish has made a £6m move for Zamora as Fulham could lose their star striker.
But Fulham have already drawn up a list of transfer targets they are pursuing, despite not having a manager.
England international Cole is top of Fulham's transfer hit-list with West Ham ready to sell for around £9m.
