Weekend reports hinted the former England boss could be mulling over his future after coming to realise the job was not as first advertised.
However, Trembling insists Eriksson is happy and will not be joining Sol Campbell in walking out of Meadow Lane.
The Magpies chief had a long conversation with Eriksson on Saturday and he is of the firm belief that the club's director of football is staying put.
"He's not. Absolutely not," he told Sky Sports News when asked if Eriksson was quitting. "It's paper talk. I'm not sure where they get all these stories from.
"I spoke to Sven on Saturday afternoon. He was talking about the under-15s game that he's going to this morning and then we were talking about the injuries ahead of our game with Torquay.
"We spent the rest of the time planning a business trip overseas in a couple of weeks, so we were just talking about that and what we want to achieve on it. So hardly the actions of a man about to leave.
"He's part of the project. It's a five-year plan. Sven's point of view is he wants us to get into the Premier League in three years, which I think is slightly ambitious, but I'm happy to take that if it happens."
Trembling insists Campbell's surprise walk-out on the ambitious club has not impacted Eriksson's position and that a number of various rumours this week are also untrue.
"Sol was here for five weeks and then decided it wasn't right for him and he decided he wanted to move on. It's completely different the two aren't linked whatsoever," he added.
"That's unfortunate - I guess that people draw too much conjecture from that and try and link everything in.
"This week we've been linked with names like David Platt and Iain Dowie and all sorts of other names, which isn't true and this isn't true either."
Meanwhile, Trembling hopes question marks over the club's ownership have finally been answered following the latest round of talks with the Football League this week.
"I don't think the questions do remain. We've been with the Football League this week and given significantly more information," he said.
"They are happy with what we've given them. They've asked for further clarification on a couple more details which we'll be supplying on Monday and that should clear it up.
"I've said all along it's a private investment trust. It's not as straight forward as some ownerships, but there will perhaps be more of these coming in anyway."
Notts Co. 4/11, Draw 7/2, Torquay 8/1