It’s understood the attacking midfielder will link up with the Black Cats' under-23s in pre-season as he bids to win a deal.
Lee came through the youth ranks at Fratton Park and made two first-team appearances off the bench in the Papa John's Trophy in the 2020-21 campaign.
The South Korean-born teenager was one of two players to be offered a new contract amid an academy player overhaul this summer.
Lee was tabled third-year scholarship terms to remain at Fratton Park – along with Harrison Brook.
However, both turned offers down and opted to depart Pompey.
Lee recently had a trial with Brentford but was unsuccessful.
Now he'll be hoping to impress the Blues' League One rivals as he targets linking up with their development squad.
Should the 17-year-old earn a contract at Sunderland Pompey will net a compensation fee.