The 20 year-old midfielder is eager to find a new challenge ahead of next season following a frustrating end to his recent campaign in north London.
He grew increasingly frustrated with his limited playing time and was frequently deployed outside of his preferred position as a deep-lying number six.
The Swedish player still managed 23 appearances for the Premier League side last term despite missing two months of action following major ankle surgery.
Representatives acting for the player have already held preliminary discussions with several top-flight rivals including Aston Villa and Nottingham Forest to gauge their interest.
Chelsea were also approached by the player's camp but the west London club chose not to pursue a deal after briefly exploring a move in January.
Tottenham Hotspur are actively looking to strengthen their own midfield options and recently launched a substantial transfer bid to secure a high-profile replacement.
The north London club submitted an offer of around £80 million for Newcastle United midfielder Sandro Tonali which was swiftly knocked back by the Tyneside club.
Bergvall is currently away on international duty representing his country at the World Cup in North America.
The young midfielder featured prominently during Sweden's heavy 5-1 loss against the Netherlands in their recent fixture held in Houston on Saturday.
His long-term future at the stadium remains highly uncertain as his representatives continue to look for alternative destinations before the transfer window closes.
The player wants regular first-team football in his natural midfield role and feels a permanent move away is necessary to develop his career.
Spurs are reluctant to lose a young talent but their pursuit of expensive alternatives signals that the player may find opportunities even harder to come by next year.