The Daily Mail reports that the Black Cats boss is ready to offer £6million for Onuoha, who has impressed while on loan at Sunderland this season.
Bruce is also keen to bring in England winger Johnson on loan for the rest of the season.
Johnson came close to joining Sunderland in a £6million deal when he left Middlesbrough a year ago.
But the 23-year-old ended up joining City in a £8million deal.
