Sky Sports is reporting that the north London duo are both monitoring the 25-year-old as Unai Emery and Mauricio Pochettino look to improve their respective defences.
The same article states that Spurs have been long-term admirers of the Germany international after watching Ginter before his move to Monchengladbach from Borussia Dortmund in a £15m deal in 2017.
According to the same story, Ginter could be a potential recruit for Tottenham as Pochettino looks to prepare for the possible departure of Toby Alderweireld.
The Belgium international is set to become a free agent at the end of the Premier League season when his contract expires.
Arsenal have a dismal defensive record in the Premier League this season despite Emery signing five new players in the 2018 summer transfer window.
Emery brought in German goalkeeper Bernd Leno, Borussia Dortmund defender Sokratis Papastathopoulos and Juventus defender Stephan Lichtsteiner.
But the Gunners have conceded 36 goals in 25 games in the Premier League this season to leave Unai Emery’s side in sixth spot.
Tottenham, on the other hand, have the fourth best defensive record in the top flight behind Liverpool FC, Manchester City and Chelsea FC.
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