The News of the World says Keane contacted the Portsmouth hitman earlier this week.
But the free transfer was held up as Cole, 35, thrashed out a six-figure pay-off from Pompey.
That has now been resolved and Cole is expecting to sign a one-year deal worth £32,000 a week with the possible option of a further 12 months.
A close friend of Cole's said: "Andrew is quite surprised by Roy's interest but he didn't have to think too long about making a decision.
"He thinks Sunderland are going places."