The report claims the Championship side are hopeful of completing a deal for the Spaniard after receiving a hefty cash windfall following the sale of Jordan Rhodes to Middlesbrough.
Blackburn boss Paul Lambert has made it clear how selling Rhodes could be the catalyst for a squad rebuild, yet he has had to hold tight with the striker only just completing his move to the Riverside.
Gomez is currently out of favour with the Black Cats, spending much of the season looking in from the outside as he struggles to break in to the 18-man match-day squad.
That said, the playmaker boasts plenty of talent and was a key player for fellow Lancashire side Wigan Athletic during their former years in the Premier League.
Gomez came through the Barcelona youth academy and spent five years at the DW Stadium, helping Wigan claim a shock FA Cup triumph under then-boss Roberto Martinez.
Blackburn will be hoping long-term to emulate their success in the top-flight, yet Lambert knows he has quite a job on his hands to turn things around at Ewood Park.
Sunderland have been extremely busy during the January transfer window, and with as many as five players moving to the Stadium of Light, Gomez has fallen further down the pecking order.
The 30-year-old has made just six league appearances for the Black Cats this term.