That's according to reports in Germany, with Glasner yet to sign a contract extension after winning last season's Europa League.
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Spurs appear likely to sack current head coach Conte following a sensational outburst after a 3-3 draw with Southampton.
His side were leading 3-1 in the Premier League clash with 15 minutes to go but they then surrendered that advantage and left with a single point.
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Conte then launched an attack on his players calling them 'selfish' and saying they can't play 'under pressure' before questioning why the club can't win trophies under its current owner.
talkSPORT understands that the Italian is now set to be sacked after 16 months in the dugout, with the majority of the club's hierarchy keen for him to depart during the two-week international break.
A number of names have been linked with the post, including former manager Mauricio Pochettino, as well as current assistant manager Ryan Mason.
Now Sport BILD in Germany reports that Spurs have made contact with Frankfurt's Glasner, whose current deal in the Bundesliga expires next summer.
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The 48-year-old Austrian had a similarly controversial press conference to Conte's after a 2-0 defeat to Union Berlin at the weekend, putting the latest links in a new light.
In a media session that only lasted four-and-a-half-minutes, Glasner said "You could play 0-0 in a game like this - but we can't. That is also a question of quality."
He added: "I don't know how you can train quality."
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Since moving from Austria to Germany in 2019, Glasner has managed Wolfsburg and Frankfurt, culminating in an impressive Europa League triumph with the latter last season.