The 33-year-old left Chelsea to join Chinese Super League outfit Shanghai Shenhua in the summer, but reports have suggested that the Frenchman is keen to return to London.
"He's a fantastic player. I would love him to come to West Ham. He'd add another dimension. He's very quick, he knows where the goal is and he brings others into play," Dicks told talkSPORT.
"He's been at quite a few clubs, and there are reasons for that, but if West ham could get him then I'm all for that."
Anelka has also played for Bolton Wanderers, Liverpool and Arsenal.