Championship promotion hopefuls Reading are said to have expressed an interest in Vaughan, who has also attracted attention from Premier League new boys Hull City and Crystal Palace.
He will face added competition for places this season if he remains at the Stadium of Light, with Di Canio having overseen a major summer rebuilding job on Wearside.
The Italian is, however, of the opinion that his efforts during the current transfer window have taken Sunderland up to where they need to be in terms of numbers.
For that reason, he is hoping to avoid seeing any departures sanctioned before 2nd September.
He said: "I don't expect many players to leave before the transfer deadline.
"A lot of players leaving is simply not part of the plan - we do not have a big squad. I'll look to make the most of every player."