Former Sunderland manager Roy Keane, now in charge at Portman Road, has made a joint bid to recruit the two men after a dreadful start to his side's Championship campaign.
Four games into the new season and Ipswich are struggling at the wrong end of the table.
Keane's men have picked up just one point after losing to Coventry, Crystal Palace and West Brom and managing a goalless draw with Leicester City.
Ipswich also crashed out of the Carling Cup on Tuesday night, losing 2-1 to Peterborough, and so Keane has turned to the core players who helped him achieve promotion while Sunderland manager, but are now considered surplus to requirements at the Stadium of Light.
Leadbitter, a product of Sunderland's Academy, has played only a peripheral role so far this season following the summer arrivals of Lee Cattermole and Lorik Cana.
Trinidad and Tobago international winger Edwards, who was signed by Keane from Luton for £1.4m in Jan 2007, played a major part in the club's promotion campaign that season, but has been unable to command a regular place in the starting line-up in the Premier League.
Bruce said: "We have given both players permission to go and speak with Roy. We'll see what develops after that."
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 £2 million permanent switch to the KC Stadium.
However, he said he was not aware of suggestions that Ipswich were also interested in defender Nyron Nosworthy and striker Daryl Murphy.