Spurs are continuing negotiations with Forest for the 22-year-old, who is valued at £50million by the Midlands club, and are hopeful of agreeing a deal — although they still need to make room in their squad by offloading a host of unwanted players.
In a bid to knock down Forest's asking price and clear the decks, Spurs have offered players in part-exchange, including Davison Sanchez.
Johnson is understood to have stated a preference for joining Spurs, while Ange Postecoglou is a big fan of the Wales international.
As a young, homegrown player, who can play across the front line, Johnson fits the bill for Postecoglou's new-look side, with Spurs aiming to dramatically lower the age profile of the squad in the wake of Harry Kane's £100m sale to Bayern Munich.
A product of Forest's academy, Johnson has made 108 senior appearances for the club, scoring 29 goals and providing 12 assists.
Brentford saw three bids for Johnson rejected by Forest, the latest worth a reported £43m, and are now understood to have moved on to other targets. If Forest agree to lower their asking price before Friday's deadline, the Bees could yet renew their interest but want to secure more firepower to cover the absence of the suspended Ivan Toney. Brentford, who have also bid for Fiorentina's Nicolas Gonzalez this month, have been linked with PSV Eindhoven winger Johan Bakayoko and Lyon's Bradley Barcola.
Meanwhile, Leeds are in talks with Spurs over a loan deal for unwanted defender Djed Spence.
The Championship club want the 22-year-old for the season on a straight loan deal, without an option or obligation to buy him next summer, with talks continuing.
Leeds have already signed defender Joe Rodon from Spurs on a straight loan deal until the end of the campaign.
Spence was reluctant to drop back down to the Championship, having joined Spurs from Forest in a deal worth up to £20m last summer, but has been told he is not part of Postecoglou's plans.
Spurs are also looking to offload Sergio Reguilon, Tanguy Ndombele, Hugo Lloris and Japhet Tanganga. Manchester United have been offered the chance to bid for Spurs midfielder Pierre-Emile Hojbjerg in the final days of the transfer window.
Hojbjerg would like to leave Spurs, where he is no longer guaranteed to be first choice in midfield and has two years remaining on his contract.
The Dane previously worked with United manager Erik ten Hag when the Dutchman was in charge of Bayern Munich's B team.
Postecoglou is confident that Spurs will resolve the futures of a handful of unwanted players, including former club-record signing Ndombele, before Friday's deadline.
"Tanguy is in a boat with a few other guys," Postecoglou said ahead of tonight's Carabao Cup second-round tie at Fulham. "I said the other day that we've got five or six players more than we can name on a list.
"All these things come down to decisions that people make, whether it's individual players, whether it's myself. We've got four or five in that boat. I'm sure this week those kind of things will work themselves out.
"He's still training. He's working hard at training. But that midfield area, we're going really well at the minute.
"You saw the guys who started on Saturday, Skippy's been really good, Pierre and Gio [Lo Celso] have been training well. It's been pretty competitive in that area. I think this week a lot of those things I expect to get resolved."