James will travel to Parkhead to discuss his future with Celtic boss Neil Lennon after Portuguese talks between his agent, Colin Gordon, and Black Cats boss Steve Bruce failed to produce a successful outcome.
With Craig Gordon expected to miss the opening month of next season with an arm injury, Bruce is keen to sign James as an experienced alternative to the untried Simon Mignolet.
However, the Sunderland boss is reluctant to match James' wage demands the 39-year-old is understood to have been on around £50,000-a-week at his previous club, Portsmouth and is unable to offer the veteran anything more than a one-year deal.
Therefore, James will head to Scotland this morning in an attempt to thrash out an alternative agreement with Celtic.
Bruce will also turn his attention elsewhere, with moves for John Mensah and Charles N'Zogbia remaining alive despite the difficulties that have been encountered in negotiations involving both players this summer.
Sunderland officials discussed N'Zogbia's position at Wigan during the talks that resulted in Titus Bramble's arrival on Wearside, but feel Latics chairman Dave Whelan has placed an unrealistic price on the Frenchman's head.
Whelan is hoping to receive around £10m for N'Zogbia's services, a price the Black Cats feel is too high.
The chances of Mensah returning to the Stadium of Light appeared to have receded when Bramble signed a four-year deal last week, but the Ghana international remains one of Bruce's leading targets following his successful loan spell last season.
Tellingly, Mensah refused to return to Lyon for the start of pre-season training at the end of last week, and despite the defender's much-publicised injury problems, Bruce is still hoping to strike a deal that is acceptable to all parties.
We are still trying to make something happen there and the talks are ongoing, he said. We all know the lad has fitness problems but I don't think there was a better defender at the World Cup.
With Bramble still recovering from a broken foot, Sunderland's lack of defensive options was underlined at the weekend as Kenwyne Jones was forced to appear as a makeshift centre-half during the pre-season victory over Hull.
Jones lined up alongside Anton Ferdinand in Albufeira as Marcos Angeleri made his first Black Cats appearance at right-back and Egyptian Ahmed al-Muhammadi started on the right of midfield.
Jones performed creditably enough in an unfamiliar role, but the Trinidad &Tobago international can hardly have been enamoured at the switch. With Stoke still being linked with a big-money bid for his services, there is every chance of the striker leaving the North-East before the transfer window closes at the end of next month.
He has already fallen below Fraizer Campbell in Sunderland's attacking pecking order, and as if to underline the fact, the former Manchester United trainee scored four first-half goals as the Black Cats briefly ran riot on Saturday night.
His first two strikes came courtesy of intelligent approach play from Steed Malbranque, while his third was a fierce left-footed drive that rounded off a fine attacking dribble.
His fourth goal, which came ten minutes before the break, was a deft header from Malbranque's floated cross.
Hull scored with a Craig Fagan penalty and Nicky Barmby's close-range strike, but Bruce was left purring over Campbell's explosive display.
We were very sharp and very cutting up front, and Fraizer gave a master class against his old team, he said. He was electric and what did he get four in 35 minutes it was a terrific performance.
He's looked very sharp all through pre-season and all of a sudden, even though he's a young boy and we know that, he looks like a man. His movement and pace was fantastic.
We also had the two new lads making their debut down the right-hand side and Kenwyne playing centre-half who I thought was terrific so there's much to think about.
SUNDERLAND (4-4-2): Mignolet; Angeleri (Kay 70), Ferdinand, Jones, Bardsley; Al-Muhammadi (Weir 70), Henderson, Zenden, Malbranque, Waghorn; Campbell (Bent 70).
Sub (not used): Carson.
HULL (4-4-2): Myhill (Duke 46); Zayatte, Gardner (Cooper 46), McShane (Barmby 46), Dawson (Devitt 65); Garcia, Ashbee (Olofinjana 57), Cairney, Kilbane; Fagan (Atkinson 57), Folan (Cousin 57).
Subs (not used): Halmosi, Emerton, Cullen.