Trembling told the Nottingham Post: "I don't want to say too much until it is over the line because of what has happened over the last six months.
"The promises I make will be because the deal is done and dusted, but we are pretty close and I am confident of getting something signed and sealed this week.
"There are a number of interested parties looking at the football club at the moment and we met one of those on Friday. There are two or three others who are very seriously interested."
County are in need of a cash injection after being hit with a second winding-up petition from HM Revenue and Customs for unpaid tax bills, and the club have been struggling financially since Trembling performed a management buy-out from Swiss-based Middle East consortium Munto Finance last month.
Trembling insists the size of investment the club is seeking is not simply to pay off its creditors but to also secure its long-term prosperity.
"We would not have embarked on this process if it was just about a short-term fix. This is about getting a deal that is right for the long-term future of the football club," he said.
The Magpies are also still searching for a new manager following Hans Backe's departure a month ago.