Gilmour is keen to go out on loan to get regular football in the second half of the season as he looks to cement his place in the Scotland squad for the Euros.
Tuchel left the 19-year-old out of the Chelsea squad for his first game in charge against Wolves on Tuesday.
His chances in the first team may be more limited under the new Chelsea head coach, with N’Golo Kante, Jorginho and Mateo Kovacic ahead of him.
Tuchel has revealed Chelsea have “absolutely no need” to let anyone leave.
But he is unsure whether Gilmour has the “physical level” to play central midfielder in the Premier League.
Tuchel said: “I have a good impression. He is a very strategic guy, very high level of game understanding.
“Very good in the first contact. Very clever in positioning.
“We will see if he has the physical level to compete in the centre of the field in the most physical league in the world. We will see that.
“But he is super quick, super-fast with his feet, super-fast with decision making and very good in positioning.
“For me, we have 21 or 22 outfield players available, playing three competitions, there is absolutely no need we have to get rid of players.”