Bruce confirmed that the Blues have tabled a bid of around £1.3 million for the former Bradford City striker who has bagged 13 goals in 28 appearances for the Clarets so far this season.
“We need some cover in attack and Robbie is bright and lively and has scored a lot of goals in his career," the Blues boss has said.
"He has got good pedigree and we like the way he plays. He would fit in with us perfectly.”
Blake was surprisingly only an unused sub in Burnley's 1-0 win against Wigan Athletic at Turf Moor on Tuesday.
The two respective clubs chairmen are now discussing the deal which if it can be can be finalised could well mean Blake is a Blues player by the time they face Newcastle at St James Park on New Years Day - the same day that the winter transfer window opens.