The North London club believe the Leeds United defender should have received a red card after catching Tel on the back of the ankle with his studs during Saturday's match.
It is understood Tottenham will write to refereeing body Pro Ref to seek an explanation for why the incident did not result in Bogle's dismissal. The club's move follows a decision that left them questioning how a challenge they consider worthy of a sending-off was assessed.
The incident was reviewed thoroughly by the Video Assistant Referee, but referee John Brooks was not instructed to visit the pitch-side monitor. Bogle therefore escaped any punishment, despite the lengthy examination of the challenge.
Former Premier League assistant referee Darren Cann supported the view that the Leeds defender should have been dismissed, describing him as fortunate to remain on the pitch.
"Bogle's challenge meets the criteria for serious foul play as he endangers the safety of an opponent," Cann told BBC Sport. "He can consider himself lucky to still be on the pitch."
Tottenham's complaint is expected to focus on the decision-making process and the reasoning behind the failure to recommend a red card after the VAR review. The club are seeking clarity from Pro Ref over why the challenge was not considered sufficient grounds for a dismissal.
The incident came at a damaging point in the first half. By the time play resumed, fewer than nine minutes remained before the interval, with Tottenham's momentum and composure fading.
Roberto De Zerbi's side did not recover after the break and were outworked and outplayed by Leeds, eventually losing the match. However, the Tottenham manager was reluctant to use the refereeing decision as an explanation for his team's performance.
"We deserved to lose the game in the second half and didn't play like we can," he told TNT Sports. "It's a journey for us because we can learn from this game.
"I am sorry for the performance in the second half - we didn't play like a top team. We didn't have the right character and physicality in the second half."
While De Zerbi accepted his side's shortcomings, Tottenham's planned approach to Pro Ref makes clear that they still want answers over the decision involving Bogle and Tel.