Forest are keen to strengthen their midfield and have identified the Sweden international as a key target.
Initial discussions have taken place, with Forest understood to have made an opening attempt at a deal worth around £38 million for the 20-year-old.
However, sources suggest Tottenham's valuation is considerably higher, with the north London club placing Bergvall in the £50 million bracket - leaving a sizeable gap to bridge if negotiations are to advance.
At this stage, it is anticipated a new bid will be made soon, but sources do not believe Forest will go as high as £50 million.
The proposed move comes at an interesting time, given the relationship between the clubs following Spurs' failed pursuit of Morgan Gibbs-White last summer.
Tottenham triggered the midfielder's £60m release clause, believing they had a clear path to completing the transfer, but Forest blocked the deal and threatened legal action over alleged breaches of confidentiality, bringing negotiations to an abrupt end.
Tottenham are open to Bergvall leaving the club - but that episode inevitably forms part of the backdrop to current discussions.
Sources insist Tottenham are not approaching talks with any intention of settling old scores. They believe the price tag is a fair reflection of how he fits in the current market.
They remain open to doing business if the terms are right, and interestingly there have been some recent whispers about Spurs retaining an interest in Gibbs-White.
Bergvall had been developing as an important young player with significant long-term potential, and Tottenham's asking price reflects that belief.
Forest see Bergvall as a replacement for Elliot Anderson, who joined Manchester City for £116 million.
They must decide how much closer to move towards Spurs' valuation, with talks set to continue. A new offer is expected to be over £40 million.
Dean Jones is a transfer news and football insider for Flashscore, since 2025. He has been a journalist on leading UK newspapers and websites over the past 20 years, establishing himself as an authoritative and trusted voice in the industry.
