Former Chelsea and Bayern Munich boss Tuchel is the first German to manage England and just the third foreigner to take charge after Sweden's Sven-Goran Eriksson and Italian Fabio Capello.
Newcastle United's Eddie Howe and former Chelsea head coach Graham Potter were among those linked with the job.
"I think most would have liked an English coach or that's the general feeling I get from the masses it seems. The game is diversifying all the time and he certainly has got a record that justifies him getting the job," Everton boss Sean Dyche told reporters.
"I don't think it's disheartening, I think it's a reality for the modern game. Every pathway doesn't lead to where you want it to."
Dyche added that he did not think of himself as the right fit for England coach, saying: "It's a massively challenging job and changed over the years. At some point in your career, you'd like to have a look at but it's certainly not the right time for me.
"(Howe) was certainly one who I looked at and thought you could consider as the next England manager."
Southampton boss Russell Martin, a former Scotland international who was born in England, said there were a number of coaches from the country who were capable of doing the job.
"English managers - it's really difficult to get the opportunity to manage in the Premier League unless you take a team there a lot of the time," Martin added.
"Maybe English managers aren't given enough credit or maybe they are deemed not good enough by the most important people... In terms of (Tuchel) getting the job, I think he's a brilliant manager and will do a really good job.
"But I think it will cause a lot of interesting discussion and conversation and especially at the FA because we have a well-renowned coach education system that people come from far and wide to do, but we can't appoint someone from that."
Welshman Steve Cooper, who is manager of Leicester City and previously coached England's Under-17s, pointed to the hiring of England women's coach Sarina Wiegman (Netherlands) and England men's cricket coach Brendon McCullum (New Zealand).
"They are brilliant coaches," Cooper said.
"Maybe it's a debate for sport in general. There's always going to be a mixed opinion on it. There's always going to be that debate and I guess there's no right or wrong with that opinion.
"It's a brilliant job, the FA have appointed a top coach and a top assistant. It will be exciting to see how it goes... I really believe in British culture, I believe in the coaching education pathway."
