The singer's record company said they were hopeful the tracks, which have never been heard before, would be made public.
They also confirmed Robbie Williams was one of several artists interested in recording an unfinished Dury track.
Williams is among the stars giving their services this Friday at a memorial concert to celebrate Dury's life.
The charismatic Blockheads frontman died in March aged 57 after a long battle with cancer.
As well as his songwriting talents, Dury was also known for his tireless charity work campaigning for Unicef to eradicate polio, which he suffered from as a child.
A spokesman for his record company, East Central One, said: "There are 10 or 11 tracks floating about.
"Hopefully they will be released at some point, but it is up to Ian's family as to whether they see the light of day."
He said most of the songs were written in the months leading up to Dury's death, but there were a couple of "older numbers" that had only recently been recorded.
All the songs feature Dury on vocals and the spokesman enthused: "I have heard them all and I can honestly say they are all very good."
Full of life
He confirmed that Williams was one of several people keen to do something with the unfinished track, and he hinted: "Robbie may well record it, although it wouldn't feature on one of his own albums."
In an interview with The Sunday Times, Dury's manager Andrew King described the new songs as "very up, funny and full of life, even though he knew he was near death".
King said: "Some were virtually finished before he died, while others had not been mixed....one or two Ian didn't rate, but most he was very happy with."
Friday's gig at London's Brixton Academy was sold out within hours of being advertised.
As well as Williams, it will feature Madness, Kirsty MacColl and Dury's backing band the Blockheads.
There are also plans to release a tribute album, with different artists performing their own versions of Dury tracks.