The 31-year-old rejoined the Magpies on a one-year deal last summer, but has seen his playing time restricted this season due to injuries and is yet to register a goal for Bruce's side.
However, according to The Northern Echo, Bruce has been impressed with the Englishman's influence on and off the pitch since his return and is looking to avoid the player becoming a free agent in the summer.
The report also claims that the Newcastle manager has valued Carroll taking fellow striker Joelinton under his wing on Tyneside, with the Brazilian another one struggling for goals this term.
However, a new contract could be complicated by the futures of other Newcastle forwards, with Dwight Gayle allegedly set to be on his way out this summer.
Carroll scored 33 goals in 91 appearances for the Magpies in his first spell at the club before a £35m transfer to Liverpool in 2011. body check tags ::