The free agent yesterday underwent a medical with the Magpies who are aiming to plug the gap created by Carroll's £35m switch to Liverpool.
Finland international Kuqi is available after his contract with Championship promotion hopefuls Swansea City was terminated by mutual consent last month.
The 34-year-old has vast experience in English football and joining Newcastle would make them his 13th different club in 16 years.
He has had spells at Blackburn, Ipswich and Crystal Palace, among others, and his physical presence could give the Magpies a boost.
As Newcastle boss Alan Pardew has sought to recruit a forward in the wake of Carroll's exit, the Tynesiders have also been linked with former Middlesbrough forward Jeremie Aliadiere and Brazilian Ewerthon.
Carroll left St James' Park for Liverpool on transfer deadline day, which left the Magpies attacking line looking very light. Days later Pardew was dealt a further blow when Shola Ameobi suffered a fractured cheekbone at Fulham.
It was feared the 29-year-old could be sidelined for two months but after undergoing surgery this week, the prognosis is more positive and he could return to the squad early next month.
Knocks to Leon Best and Nile Ranger heaped further pressure on Pardew with both players pulling out of their respective international squads, but news yesterday was positive and both are expected to be fit for the trip to Blackburn Rovers on Saturday.