Forest had an opening offer of around £38m turned down, and are now working on an improved package worth in the region of £45m as they push to land the 20-year-old before pre-season progresses much further.
Oliver Glasner sees Bergvall as the ideal long-term successor to Elliot Anderson, whose British record £116m move to Manchester City left a gap in the middle of Forest's midfield that the club have prioritised filling with a genuine passer rather than a purely defensive presence.
Spurs, for their part, have given no indication they are willing to let Bergvall leave, with the club valuing him at closer to £50m. That gap in valuation is likely to be the main obstacle to any deal, even with Forest returning with a significantly improved offer and Glasner keen to get his midfield rebuild wrapped up before the season begins.
Bergvall's path to regular football has narrowed considerably since Roberto De Zerbi's arrival as head coach, with Tottenham having spent heavily this summer on Sandro Tonali and Mateus Fernandes to strengthen central midfield. That investment has intensified competition for places, and Bergvall has made his desire for a move known to the club's hierarchy despite their reluctance to sell.
Omari Hutchinson remains Nottingham Forest's current record signing at £37.5m following his move from Ipswich Town last year, a fee that would be comfortably surpassed if the Bergvall deal goes through at the reported valuation.
Bergvall joined Tottenham from Djurgarden in 2024 after beating Barcelona to his signature, and impressed sporadically in his debut season without quite establishing himself as a guaranteed starter.
He featured for Sweden at this summer's World Cup, making his first start of the tournament in the last-32 defeat to France, and returns to pre-season with his long-term future in north London increasingly uncertain.