Bolton have reportedly been in touch with Blues about talking to Bruce, who still has 20 months to run on his contract, but the Blues' board of directors are understood to have denied Wanders permission to talk with Bruce.
The Blues boss, whose future at St Andrew's remain's in doubt as prospective new owner Carson Yeung may want to bring in a new manager when, if expected, he takes complete control of the club.
Bolton, who parted company with manager Sammy Lee on Wednesday, are also understood to be keen to talk with Paul Jewel, Gary Megson, Graeme Souness and John Collins.