Trembling is in "advanced talks" with three prospective investors - one party is believed to be Norwegian telecommunications giant Ludo - and is confident of brokering a deal with one of them by next week.
That investment would see the debt paid and the transfer embargo subsequently lifted enabling the club, who are fifth in League Two, to sign players.
"As soon as we have paid that debt and satisfied the Football League it has been cleared, then the embargo will be lifted. And it is important we get it resolved next week," said Trembling.
"If we get serious investors over the line next week we have a target of five or six players we would look to bring in, maybe not all of them but four to strengthen the squad immediately."
Meanwhile, Sven-Goran Eriksson's right-hand man Tord Grip has revealed he will leave Notts County should the club fail to attract major investment before the end of the January transfer window.
Grip is general advisor at Meadow Lane and responsible for scouting players but he is unable to do that at the moment because of the Magpies' financial problems and the embargo the Football League has imposed on the club.
Trembling admitted on Tuesday that he expects Eriksson to quit unless multi-million pound investors are found, and Grip would follow his long-time friend through the exit door.
"It's very messy and a time of waiting. For me there's not so much to do because I can't buy any players," Grip told Swedish newspaper Expressen.
"We just sit in the office, it's not happening so much. The club must get more money before the transfer window is closed. (If they don't), then we don't have any money and I will leave the club."