Miguel Herrera has been fired as Mexico coach following allegations that he punched a television reporter.
Former Arsenal midfielder Abou Diaby has rejected an offer to join West Brom in favour of finding a new club in France.
The Tigers currently occupy fourth spot in npower Championship as the season's halfway mark approaches.
And Bruce is keen to inject fresh impetus into his squad to maintain their promotion push following a recent meeting with Allam.
"We've had discussions with Steve with a view to January and we have an idea of what our requirements are," the chairman told the Hull Daily Mail.
"We will be looking to give Steve our full support in the transfer window to give us that final push.
"We have every confidence in Steve. He's proved himself as a top quality manager and we'll be supporting him the way he sees fit."