Darron Gibson has made just one appearance for Everton this season in the EFL Cup
Darron Gibson and Bryan Oviedo have both been on the fringes at Everton since Ronald Koeman took charge.
Gibson has made just one EFL Cup appearance all season, while Oviedo has turned out just seven times for the Toffees.
Bryan Oviedo is also said to be on David Moyes' radar at Sunderland
"Sunderland set to sign Bryan Oviedo and Darron Gibson from Everton. Medicals today," Joyce tweeted.
It is unclear whether they will be permanent deals or loans until the end of the season.
Sunderland boss David Moyes seems keen to sign his ex-players as he prepares for a relegation scrap.
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The former Everton boss has already brought in experienced defender Joleon Lescott after he was released by Greek side AEK Athens.
And Moyes knows Gibson and Oviedo from his time at Goodison Park, prior to his move to Manchester United in 2013.
Gibson has made 69 appearances for the Toffees in four years, while Oviedo has featured 68 times since joining from Copenhagen in 2012.