talkSPORT understands the Austrian manager has agreed terms with the south London outfit to replace Roy Hodgson.
Palace sit in 16th spot in the Premier League table - just five points above the relegation zone.
And Glasner has been pictured in London attending Spurs' clash against Wolves at the Tottenham Hotspur Stadium on Saturday.
With Palace to travel to Spurs on March 2, fans believe that the 49-year-old is already on a scouting mission.
An image of Glasner and his assistant Michael Angerschmid sitting in the stands has went viral.
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Commenting on the photo, one X user said: "Nice! Good bit of prep and scouting ahead of the upcoming game!"
Another messaged: "He's here in the stands at Tottenham today. Palace play here at the start of March…"
A third added: "Guess he's checking on Spurs, we play them soon."
This Palace supporter posted: "Glasner preparing for March 2nd."
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Meanwhile another simply stated: "Work already under way."
It is believed that Glasner will put pen-to-paper on a deal until 2026 at Selhurst Park.
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It remains to be seen when a decision will be made on Glasner after Hodgson was taken to hospital having been fallen ill at Palace's training ground on Thursday.
The club later confirmed Hodgson was in a stable condition, but will not be in the dugout for Monday's clash against Everton.