The 22-year-old, who departed the Black Cats in 2012 having failed to make a first-team appearance, has also spent time with Oldham Athletic.
"I'll be talking to him over the next 24 hours to try and do something," Ward told the Bristol Evening Post.
"We are short of players now and we certainly need to look at one or two reinforcements to get us through the next couple of months.
"It's difficult because I have my full amount of loans taken up so we have to look at free agents. Oumare is a big strong boy and would be a good addition for us."
Tounkara scored seven goals during his loan spell at Oldham.