The German publication report that the deal is set for €12 million [roughly £9.1m] and that a medical is due to take place shortly, with Wolfsburg happy for the Switzerland international to leave.
Speaking to Kicker, Allofs said: “There is definite interest from Norwich City. An agreement is expected, and we are well prepared to cover in the event that it happens.”
Klose has struggled to break in to the first-team this season, making seven Bundesliga starts and finding himself behind the likes of Dante, Naldo and Robin Knoche in the pecking order.
The 27-year-old will be keen for regular first-team football as he seeks a place in Switzerland’s 23-man squad for the upcoming European Championships in France.
Klose joined Wolfsburg from Nuremburg in 2013, and helped the club win the DFB Pokal Cup last year.
Norwich boss Alex Neil has been desperate to add to his squad this month, with a new goal scorer and a top quality centre-back topping the club’s January transfer window wish-list.
Klose stands at 6ft 4inches and is strong in the tackle, reads the game well and boasts plenty of experience.