The newspaper cites two sources who claim production was originally set to begin in October, although that date has not been confirmed by the Japanese car maker.
In a statement sent to Autocar, Nissan said: "Preparations continue for the launch of the new Qashqai in Sunderland, which represents a £400m investment in the plant."
The firm added: "We have not yet announced a date for the next-generation model, but look forward to sharing some exciting news in the coming months."
The FT indicated that the apparent delay is largely due to the fallout from the coronavirus pandemic, which has delayed development and changed the firm's priorities. It suggested the delay could also allow Nissan to work out its course of action should Britain not secure a deal with the European Union post-Brexit.
Just over half of the approximately 500,000 cars produced at Sunderland annually are exported to Europe, and two-thirds of those are Qashqais. Any trade tariffs with the EU would "jeopardise" Sunderland's business model, bosses have previously claimed.
The report suggests that production of the new Qashqai will not begin until after April 2021. The current version has been on sale since 2014.