A woeful defeat to relegation rivals Nottingham Forest leaves Spurs above the Premier League's bottom three by a point.
Tottenham's near half a century stay in the top flight is under growing threat.
Victorious Nottingham Forest are on their fourth manager of the season with Vitor Pereira but Spurs may have to appoint their third to survive.
Tudor has lost five of his seven games after being appointed in February after Thomas Frank was sacked, having been hired in part for his positive short-term record at previous clubs.
If he does depart, Tottenham will have to decide whether to appoint another interim head coach or a permanent candidate with seven games left.