The defender’s deal expires in the summer, along with those of team-mates Toni Rudiger and Cesar Azpilicueta.
Chelsea boss Tuchel insisted all parties are on the same page on a new deal for Christensen, with the 25-year-old’s current contract expiring next summer.
Tuchel also remains hopeful that Toni Rudiger will extend his own Stamford Bridge deal, that also runs out at the end of the campaign.
The Blues’ German boss believes that the in-demand Rudiger knows how valued he is at Chelsea – but also that he remains focused on the “toughest challenge” of the Premier League.
Club captain Cesar Azpilicueta’s contract will also expire next summer, leaving Chelsea’s defence in a possible state of flux.
But an unfazed Tuchel insisted the Blues’ hierarchy are handling all negotiations in a calm and mature manner.
“For Andreas, from my point of view, everybody wants the same thing, the coach wants the same thing, the club wants the same thing and the player wants the same thing,” said Tuchel.
“So, hopefully and obviously I expect some good news in the next days, but every case is different. And you can end up in situations like this, but the situations are handled from all sides very carefully, very professionally and in a very mature manner.
“And so during the process we can produce performances that we need to fulfil our goals and that’s the most important thing. Things are very mature, very respectful and very clear.”
Chelsea’s out-of-contract players can talk to European rivals about a possible move from January 1, a date that naturally accelerates negotiation schedules.
Germany centre back Rudiger has thrived under Tuchel’s management style and the Blues’ 3-4-3 tactical blueprint.
The 28-year-old struggled at times under Frank Lampard but has been right to the fore of Tuchel’s set-up, with Chelsea swiping the Champions League title last term.
Tuchel remains hopeful Rudiger will sign on for more at Chelsea, but insisted no scenario in discussions will affect matters on the field this season.
“Of course there are some delays, with Toni and with Andreas in the moment, but it’s pretty clear what we want,” said Tuchel.
“But it’s not always like this in football that the coach wants something or the club wants something and then that thing happens.
“You have to accept that sometimes it can arrive and you can end up in situations where things are in a bit of a delay.
“And things maybe take their time but I’m very, very sure that Toni feels also how respected and what kind of an important role he plays for this club.
“I think he’s up for the toughest challenge, and the toughest challenge is Premier League football.
“The toughest challenge is to play Premier League football to win titles, so he’s a big part in a big club and I’m very sure that he is aware of it.
“So I’m calm, because I feel Toni is calm, I feel the situation calm inside, and from here we go.
“I’m happy that he plays how he plays and we need him on this kind of level.”