The German claimed after the 2-2 draw at Stamford Bridge on Sunday that "maybe it would be better" for the referee not to officiate Chelsea again, with the Blues boss incensed that both of Spurs' goals were allowed to stand.
Tuchel and Spurs boss Antonio Conte clashed twice on the touchline, causing two melees as tempers flared.
Both managers were booked for the first bust-up, then sent off at full-time when a niggly handshake between the pair sparked further ugly scenes.
Tuchel accepted in the aftermath on Sunday that he would be likely to face FA punishment, and now the governing body has moved to follow up with an investigation.
Kalidou Koulibaly volleyed home Marc Cucurella's corner, before Pierre-Emile Hojbjerg hit back for Spurs.
Reece James fired home to put Chelsea back in front in the closing stages, only for Harry Kane to nod home in the sixth minute of second-half added time.
Tuchel lamented both Spurs' goals being allowed to stand, claiming Richarlison was offside for Hojbjerg's effort and that after Chelsea had claimed a foul on Kai Havertz in the build-up.
The Blues were then left furious that Christian Romero was not punished for pulling Cucurella's hair, with a VAR check ruling out a red card but then not imposing any sanction.
More than 90,000 people have signed an online petition demanding Taylor be blocked from refereeing Chelsea again.
Chelsea supporters have long claimed an agenda from Taylor against them, and Tuchel did not dampen those flames when speaking after Sunday’s tetchy but compelling draw.
Asked if he thinks Taylor should not referee Chelsea again, Tuchel replied on Sunday: “Maybe it would be better, maybe it would be better. But honestly we also have VAR, to help make the right decisions.
“Since when can players have their hair pulled, since when is that? And if he does not see it, I don’t blame him - I didn’t see it. But we have people at VAR who check this, and then you see it. And then what?
“And how can this not be a free-kick, and then a red card? How? This does not even have to do with the referee in this case. If he does not see something that’s why we have people to check if this is a decisive error or not.”
When asked again about Chelsea supporters’ concerns about Taylor’s officiating, Tuchel continued: “I don’t think that just some of the fans think that: I can assure you that the whole dressing room of us, every person thinks that.
“Not only the fans. You know the players, they know what’s going on when they are on the pitch. They know it.”
Asked if the players are worried when Taylor is in charge, Tuchel added: “Yeah, of course.”
And when it was put to him that he will most likely face a touchline ban for next weekend’s Premier League trip to Leeds, Tuchel said: “So, good! I cannot coach but the referee can whistle the next game.”