Man City bid to buy Hamburger De Jong
It did not provide any details of the offer, which German media have estimated at around 15 million euros ($20 million).
"City have had contact with us, they have expressed an interest and have submitted an offer," Hamburg's sports chief Dietmar Beiersdorfer told reporters at the team's training camp in Spain's La Manga.
De Jong, whose contract with Hamburg expires next year, confirmed he had received an offer and said he still had two weeks to decide before the transfer window closes.
"I have to see what's best for me," said De Jong, who joined the Bundesliga club in 2006 from Dutch side Ajax Amsterdam.
City, in the bottom of half of the Premier League table, are the richest club in the world after being taken over by the Abu Dhabi United Group.
They are also in talks with AC Milan over an offer for Brazil playmaker Kaka, which media reports say is worth at least 100 million euros.