However, despite reports in Ireland suggesting the Black Cats have also tabled a £7m bid for Shane Long, a club spokesperson last night played down the club's supposed pursuit of the Reading striker.
Steve Bruce has stepped up his pursuit of Ipswich forward Connor Wickham and retains an interest in Liverpool's David Ngog, but at the moment, Ji is the only striker on the verge of agreeing a deal with the Wearsiders.
The South Korea international toured Sunderland's training ground yesterday morning before holding contractual talks with officials.
The 20-year-old is expected to sign a three-year contract shortly, enabling him to briefly return to his homeland before travelling back to England for the start of pre-season training.
He will be joined by fellow summer signings Seb Larsson and Kieren Westwood, and the trio could all be involved in Sunderland's opening pre-season friendly at York City on July 13.
Craig Gardner is also expected to be a Black Cats player by the middle of next month after Birmingham accepted a £5m bid for his services over the weekend.
Whether another new striker is also paraded at Bootham Crescent remains to be seen, but with Liverpool having failed to make headway in their attempts to sign Wickham, Bruce is redoubling his efforts to land the 18-year-old.
He is in regular contact with his opposite number at Portman Road, and while an £8m bid was rejected last week, an improved offer is in the pipeline.
The Sunderland boss accepts that Liverpool are Wickham's first choice of new employers, but with the Anfield club currently focusing their transfer attention elsewhere, there could yet be an opportunity to force the youngster's hand.
If, however, Wickham does move to Merseyside, both Ngog and Long remain viable back-up options. Sunderland officials are aware that Liverpool will accept £5m for Ngog, but while preliminary talks took place as Jordan Henderson completed his £19.5m move to the Reds, further discussions are currently on ice.
The striker situation is likely to remain in something of a state of flux until August, as Bruce is also keen to make one last push to re-sign Danny Welbeck on loan.
Manchester United boss Sir Alex Ferguson is expected to run the rule over the England Under-21 international during pre-season. but if Dimitar Berbartov remains on the Old Trafford books this summer, Bruce believes there is still a chance that Welbeck could rejoin Sunderland.
"This summer, we will be looking at the loan market again to see where we can gain value for money," he said. "It is an area of recruitment which has become more important in recent seasons.
"The one thing about Nedum (Onuoha) and Danny last season was that they were desperate to play regularly, and when you have that sort of hunger in a player it helps us and them. That is my thinking.
"It also helps you financially too. Imagine trying to buy Danny, Nedum or Sulley Muntari on the open market.
"The downside is the fact you rarely have them for longer than a season. But where else can you find an £8m defender or £10m striker for your squad for nothing"
Meanwhile, one player is set to leave Wearside before the end of the week with out-of-favour midfielder Cristian Riveros close to completing a deal with Turkish side Kayserispor.