Per MailOnline's Will Griffee, the Italian said he's not speaking to clubs yet, as he doesn't know what he'll do once the season is over: "I'm not talking about my future, I am not speaking about my future, as I do not know what it holds. I will be back at the end of the season even though I am getting used too well to holidays. I have to come back. I don't know my future yet."
Allegri parted ways with Juventus at the end of last season and opted to take a sabbatical.
Tuchel has come under pressure in Paris, with questions about his future should the team suffer yet another early UEFA Champions League exit. Les Parisiens have been eliminated in the round of 16 in three straight seasons, the last of which came under his guidance.
The Ligue 1 champions are once again in danger at the same stage of this year's competition after losing 2-1 in the first leg to Borussia Dortmund.
PSG played poorly in Germany, and things didn't go to plan both during and after the match:
Get French Football News @GFFN
PSG last night cont: - SD Leonardo refuses to speak to media in the mixed zone - Tuchel justifies use of 3-4-3 formation by saying he used it vs Dijon - Tuchel justifies defeat by saying that Dortmund had an extra day of recovery & played 7 less games in 2020 than PSG so far
Neymar scored but complained he hadn't seen any playing time in the four matches prior. Erling Haaland got both goals for the hosts.
PSG have a healthy 10-point lead in Ligue 1, but the club is hungry for continental success after dominating the domestic scene for years. They have won six of the last seven league titles.
If they fall flat in Europe this season, a coaching change seems likely. And while Allegri was unable to guide Juventus to a UEFA Champions League title, he did take the Bianconeri to the final twice.
In his five seasons in Turin, he won the Serie A title every time and did the Italian double in four straight seasons.
His stats compare favourably to those of his replacement, Maurizio Sarri:
Allegri also secured three top-three finishes with Milan, including the 2010-11 Serie A title.
He's likely to be a popular target for several top clubs looking for a new manager in the summer, and Corriere della Sera (h/t Sport Witness) reported he already has an agreement with a team from England:
Allegri isn't expected to commit to a club until the end of the season.