The newspaper says Ferguson believes the 25-year-old could be the final piece in his Manchester United jigsaw.
Saviola will quit Barcelona this month on a Bosman free and could be heading for Old Trafford for less than £7 million.
United would be prepared to offer Saviola a contract for around three years and worth about £50,000 a week.
Arsenal, Liverpool, Bolton, Valencia and Real Madrid are all interested in signing but News of the World says Saviola’s preferred choice is United.