The Black Cats were increasingly linked with both players in last years summer transfer window, and now - if reports are to be believed - Gus Poyet is willing to invest €22m to rekindle that interest.
Sow and Meireles helped Fenerbahçe to their 19th Süper Lig title this season, but after the Turkish giants received a two-year ban from European football for match fixing in August, both may be tempted to play their football elsewhere.
Sunderland severely lacked in attacking quality last season, eventually relying on a late spurt of goals from youngster Connor Wickham to survive relegation after Jozy Altidore and Steven Fletcher managed only four league goals between them.
Sow could finally provide an answer to Sunderland's goal-scoring problems; the Senegalese striker has contributed 15 league goals in consecutive seasons at Fenerbahçe and appears to be in the peak of his career at 28-years-old.
Meireles is part of Portugal's 23-man squad for the upcoming World Cup in Brazil and carries with him some Premier League experience. The midfielder enjoyed short spells at both Liverpool and Chelsea, winning a Champions League title with the latter before departing for Turkey in 2012.
Having just achieved their second great escape in consecutive seasons, there is much rebuilding to be done at Sunderland if they are to progress to the higher reaches of the Premier League.
But the club will feel empowered by the fact that Brand Finance listed Sunderland AFC as 31st richest in the world last week, and if reports in Turkey are anything to go by, the Black Cats won't be shy on spending big this summer.