Luxury carmaker Audi
The unit of Volkswagen
The purchase, which will add expertise in high-revving light engines to VW's wide-ranging engineering portfolio, could be announced as early as April 18, the day before VW's annual shareholders' meeting in Hamburg.
One of the sources said that Ducati's main shareholder, Italian buyout firm Investindustrial, agreed to talk with Audi exclusively.
Volkswagen, Audi and Investindustrial declined to comment.
VW chairman Ferdinand Piech, a former chief executive officer of Audi, has long coveted Ducati for its expertise on design and light engines.
Ducati would increase the VW group's brand portfolio to twelve, a number which Piech has said would be the right size for the German automotive group.
If Piech wants it, he will get it, said a banker who is familiar with the matter.
Italian newspaper Corriere della Sera also reported on Wednesday that an accord between Ducati and Audi was expected to be signed next week, citing no sources.
The paper noted that Audi had the right to negotiate exclusively until April 15, after which Investindustrial was free to talk to other potential buyers.
In 2005, Audi tried to buy Ducati from former owner Texas Pacific Group but was trumped by Investindustrial, Corriere della Sera added.
Ducati, founded in 1926, has won 17 manufacturer's World Championship titles over the past 60 years, most recently the 2011 World Superbike trophy.
Investindustrial's chairman Andrea Bonomi told The Financial Times in February the firm was looking to sell Ducati.
Last month the paper cited sources as saying the price could be about 850 million euros ($1.1 billion) including 800 million in acquired debt.
The two sources on Wednesday declined to comment on the purchase price or give more details.
For Audi, whose Ingolstadt headquarters has become a key research and development centre for lightweight fuel saving technologies, Ducati's engine technology could add a new development dimension.
Audi has also owned Lamborghini since 1998 and together with the Italian supercar maker aims to produce lower weight vehicles by increasing the share of components made of carbon fibre.
($1 = 0.7644 euros)
(Additional reporting by Andreas Cremer in Berlin and Jennifer Clark in Milan; Editing by David Cowell)