
The London club are holding talks with the Baggies over the proposed transfer of the Chinese captain.
Zheng joined Charlton in December 2006 on loan and was subsequently signed permanently the following summer despite the fact that the Addicks were relegated to the championship.
The midfielder’s impressive performances in the second tier have alerted West Brom.
"We are in discussions with West Brom and they are ongoing," said Charlton coach Alan Pardew.
"There are lots of discussions on all sides, but I don't think it's anything to do with the work permit because he's the China captain and their best player.
"I don't think there is a problem with that, it's just between ourselves and West Brom, taking into account the player's commitments as well."