The German website SportBuzzer reports that the 44-year-old Bavarian has already signed a two-year contract.
In France, the sports daily L'Equipe quibbled over the details, saying it is "premature to say the deal is signed" but "it's only a question of timing", probably at the end of the season.
Emery appears to be merely biding his time in the PSG hotseat after the crushing elimination from the Champions League at the hands of Real Madrid.
Tuchel's modest playing career peaked early with a handful of matches for Stuttgart Kickers in the German second division in 1992-93.
He went on to coach Mainz and Borussia Dortmund, winning the German Cup after succeeding the highly successful Jurgen Klopp.
Tuchel was recommended to the camp of emir Tamim ben Hamad al Thani by the Qatari consul to Germany, L'Equipe reported. He would be the first German to lead PSG.
Tuchel has been without a club since his tumultuous departure from Dortmund in May 2017 after a series of public disagreements with the club's chief executive.
Bayern Munich tapped up Tuchel recently as a possible successor to 72-year-old Jupp Heynckes, who insists he will not stay. But Tuchel "was already signed with a club," said Bayern chairman Karl-Heinz Rummenigge.
This interest from big clubs shows Tuchel's standing despite his lack of trophies. That German Cup run included a 3-2 victory over Bayern Munich in a crazy semifinal.
He also led Dortmund to second behind Bayern in the Bundesliga in 2016.
Tuchel is famed for his passion for tactics. Niko Kovac, who manages Eintracht Frankfurt, the losing team in last year's German Cup final, called Tuchel a "chorus master" and praised his "genius for playing different systems week after week."
Tuchel also has a reputation for man management, especially with younger players, and attracted attention at Dortmund for the spectacular way he developed such rising stars as Ousmane Dembele, now at Barcelona, US international Christian Pulisic and Julian Weigl. But Tuchel reportedly had difficulties with veteran players he wanted to phase out.
This profile as a tactician and demanding, even authoritarian, coach calls to mind Pep Guardiola who works at Manchester City for the Emiratis, the great regional rivals of the Qataris, and is poised to add the Premier League title to his collection of titles.
Dressing room of divas
Guardiola has won the Champions League. Tuchel has never progressed beyond the last eight of the trophy PSG's owners most covet. Emery arrived in Paris with three Europa League titles but remains the man responsible for the "Remontada" when PSG blew a 4-0 lead against Barcelona, losing the second leg 6-1 last March.
One reason offered for Emery's difficulties in Paris is a lack of experience handling a squad of stars. Tuchel had Pierre-Emerick Aubameyang, a star with a big ego in Dortmund who is now at Arsenal, but PSG has a dressing room full of divas.
Neymar's entourage reportedly pushed for Luis Enrique, the former Barcelona coach who won the Champions League with the Brazilian in his team in 2015.
Meanwhile veterans such as Thiago Silva, and the Italian playmaker Marco Verratti, have let it be known that they favoured the return of Carlo Ancelotti, who managed the Paris club from 2011 to 2013.
SportsBuzzer says Tuchel is already working on what he needs to do at PSG. But history suggests he won't have much time to show he can do better than Laurent Blanc who took PSG to the Champions League quarter-finals in 2015 and 2016 and was fired in June 2016.
For PSG, Tuchel represents another long-odds bet, but the prize, for both sides, remains huge.