West Brom coach Darren Moore is happy to stay at the Hawthorns.
Moore has been linked with the manager's job at Barnsley.
The Express & Star says Oxford United and MK Dons have also made enquiries about his availability in the past year.
The Dons also made a brief enquiry before Dan Micciche was appointed last month.
Rodriguez has been charged for alleged racial abuse of Gaetan Bong, although the 28-year-old has vowed to fight the charge and prove his innocence.
"It's a situation which is not ideal for Jay," said Pardew. "It's an accusation he denies and we're going to support him.
"It's a process which needs to be seen through and our comments can affect it so the less we say the better.
"Jay is upset about it, he has a good mental capacity to deal with things and hopefully he can concentrate on his football and not worry too much - although it is a worry.
"At the moment he's angry but he's ok."