Sebastian Coates and Adam Matthews have been confirmed, with more set to follow.
The Black Cats travel to North America on Sunday, before returning twelve days later, and the Dutchman is expecting deals to be done by then.
“We will definitely have some more by then (the time they return from North America) or there is something wrong,” said Advocaat, in an interview with the Sunderland Echo.
He made sure to highlight that his approach to the transfer window was not a reckless one, however, adding: “But then on the other hand, if I cannot get the right players, I don’t buy them. I don’t like to waste money.
“I’m looking for players that I know will make the team better. That’s it, not the same level, a little bit better.”
Both players would be great additions to the Sunderland squad and a deal for Lombaerts looks closer to completion, with Besiktas threatening the Lens move, as per the Sunderland Echo.
The Black Cats have reacted and remain confident of getting their men, however, launching an improved £9 million bid for Lens in a bid to fight off rival interest, according to the Daily Mail.
Sunderland fans will be hoping Advocaat's words prove to be true as they look to kick on again next season and build upon a decent end to the last Premier League campaign.