HITC Sport understands that Black Cats are hopeful of concluding deal.
Sunderland have made a fresh move for Andre Ayew by bidding £10 million plus Fabio Borini, HITC Sport understands.
The Black Cats first made a move for Ayew earlier this month, but were rebuffed by their relegation rivals - but their interest has not waned.
Indeed Sunderland have now returned with an increased offer, plus Borini - who has experience of playing in South Wales.
During his time at Chelsea, Borini spent half-a-season in South Wales and was a major success, and he is still remembered fondly at the Liberty Stadium - one reason that Sunderland have now made the offer including him.
Sunderland are now waiting for a response from the South Wales outfit, but sources close to the North East club have told HITC Sport that they are willing to go higher to land Ayew.
Ayew only joined Swansea in the summer when he arrived on a free transfer from Marseille, but despite their struggles he has performed very well with 8 goals in 22 starts.
Like Ayew, Borini only finalised a move to Sunderland this summer when they paid Liverpool around £8 million to land him, but he does not appear to figure in manager Sam Allardyce's long-term plans.