Isn't Tuchel's deal 18 months? So it's almost certain the FA did speak to Pep, it's also almost certain that he'd have been offered the job if interested however given the fact Tuchel's deal is 18 months maybe he's indicated to the FA that he'll stay at City for another season after this one.
Just my own musings, not based on anything I've heard.
Re the next City manager, despite the current rancour almost certainly Arteta would be an option - whether he'd take it if still at Arsenal I don't know but if he wasn't at Arsenal he'd take it if offered.
Inzaghi at Inter would be an option, I'd rule out Amorim though - you don't go from Sporting to City without a step in between. Who I get a hunch City would target however would be someone like Nagelsman the Germany coach. He plays the right type of football, is still young but garners respect.
Ancelotti is maybe too old to take on a project like City for 5+ years.