Lorient's Benjamin Moukandjo
The same source credited the Black Cats with an interest in Moukandjo on Thursday, and the trio are now said to be considering bids for the Cameroon international.
Lorient reportedly value Moukandjo, a reported target for Crystal Palace earlier this year, at £8 million.
All three clubs are in need of attacking reinforcements this summer. Sunderland's move for West Ham United's Diafra Sakho is said to have stalled, while Swansea are set to lose Bafetimbi Gomis to Marseille (L'Equipe) and Saido Berahino has turned down the offer of a new West Brom contract (Sky Sports).
Diafra Sakho's exit is reportedly held up by West Ham's failure to land their own striking targets
And Moukandjo, who scored 13 goals in last season's Ligue 1 campaign - despite missing its final six weeks through injury, is likely to fit the bill.
The 27-year-old only moved to Lorient a year ago from Stade de Reims, having previously played for Monaco, Nancy and Nimes.
He has 32 caps for the Indomitable Lions and can operate on either flank if required.
Moukandjo in action for Cameroon