As revealed by skysports.com on Wednesday, Ipswich have lined up a move for Leadbitter and Edwards after agreeing fees with Sunderland for the midfield duo.
Ipswich boss Roy Keane is determined to bolster his squad and is keen to be reunited with Leadbitter and Edwards having worked with the pair during his time in charge of the Stadium of Light.
Bruce said: "We have given both players permission to go and speak with Roy. "We'll see what develops after that."
However, he said he was not aware of suggestions that Ipswich were also interested in defender Nyron Nosworthy and striker Daryl Murphy.
Bruce also confirmed that defender Paul McShane has had a medical at Hull, where he spent the first half of last season on loan, with a view to completing a £2million permanent switch to the KC Stadium.
The Black Cats chief is believed to be in the market for a new defender, but he has ruled out a move for Portsmouth's Sylvain Distin because of the asking price for the Frenchman.
"There's nothing there. The valuation, in my opinion, is too high for somebody who is nearly 32-years-old," added Bruce.