The two London rivals are thought to be among the top-flight clubs keeping a close eye on the 20-year-old Englishman, who has excelled for Nuri Sahin's side in the 2024-25 season.
Gittens has scored nine goals and set up four more in 22 appearances across all tournaments this term, including four strikes in the Champions League, one of which came away to holders Real Madrid.
Gittens - who previously represented Reading and Manchester City before moving to Dortmund in 2020 - has a long-running contract with the German giants, who will not lose him until 2028 as things stand.
However, Dortmund's resolve could very well be tested next summer, where Liverpool, Tottenham Hotspur and Aston Villa could also rival Arsenal and Chelsea for Gittens's signature.
Dortmund would "politely decline" £40m Gittens offer
The quintet would have to pay a pretty penny to prise the 20-year-old away from Signal Iduna Park, though, as Dortmund managing director Lars Ricken has insisted that £40m would not be enough for his side to consider a sale.
Asked by SportBILD if that price tag would suffice, Ricken replied: "I wouldn't hang up immediately because that would not be in keeping with my character. But I would politely decline," as quoted by BirminghamLive.
Fellow club chief Carsten Cramer has also expressed optimism that Gittens will choose to snub interest from the Premier League to stay at Dortmund, who have a rich history of developing young talents into world-class players.
Gittens joined Dortmund on a free transfer after being cut from Man City's academy, and the London-born winger now has 14 goals and 13 assists to show from 80 appearances for the club in all tournaments.
Gittens has also won 11 caps for the England Under-21 team and was a part of the Under-19s side that won the Euros in 2022, starting in the Three Lions' win over Israel in the final.
Which club needs Gittens the most?
The right-footed winger is capable of doing a job on either flank, but he has been predominantly deployed on the left-hand side this season, making him an intriguing option for Arsenal in particular.
Neither Gabriel Martinelli nor Leandro Trossard - now in his 30s - have been cutting the mustard this season, and Raheem Sterling will be returning to Chelsea when his loan spell ends.
Ten years Trossard's junior, Gittens could be a natural successor to the Belgian in North London if Arsenal decide to pursue a more youthful option, but Spurs and Liverpool may also be after a new left-winger in 2025.
Tottenham skipper Son Heung-min is expected to stay on until at least 2026 as Spurs prepare to trigger his contract extension, but it is not clear if he will stick around for any longer, and Timo Werner's loan from RB Leipzig is unlikely to be made permanent.
Meanwhile, Liverpool's Luis Diaz has been strongly linked with moves to Barcelona and Paris Saint-Germain, and the Reds are supposedly struggling to make progress in contract talks with the Colombian.
Written by
Ben Knapton