The 21-year-old is on loan with League One outfit Bradford City until January but could step up a division when the transfer window reopens.
According to the Chronicle, Sunderland boss Chris Coleman will enquire about the possibility of signing Gilliead on loan before firming up his interest.
Gilliead spent the second half of last season on loan with Bradford before extending the deal in the summer.
He has scored one goal and provided a further assist for the Bantams this term.
Meanwhile, Sunderland boss Coleman could have defender Marc Wilson available to face Reading on Saturday for his first game in charge at the Stadium of Light.
“Marc trained this week with us. We gave him a bit of a hit and he came through it OK,” said Coleman.
“Darron Gibson didn’t train on Tuesday or Wednesday because we trained indoors due to the weather, and not all players can train on that because of the reaction they get to working on astroturf, but he is fine.
“We’ve still got the long-termers missing such as Duncan [Watmore], and Jonny Williams is out for two or three months, Lamine Kone is out for two or three…