The former Rangers youngster caught the eye at Euro 2020 for his performance against England in the second Group match after being left out of the opening defeat by the Czech Republic and acquitted himself well at Wembley, putting in a man-of-the-match performance before he returned a positive test for Covid-19, ruling him out of the final match against Croatia.
"It was very difficult," Gilmour told Sky Sports. "The game itself I enjoyed a lot. I think on another day we could have scored. We had our chances.
"To wake up and find that I had Covid... it was annoying because I felt fine. It was not the best ending to what was meant to be a good summer."
The 20-year-old joked that he had spent most of his time on international duty finding out more about the Carrow Road outfit.
"I was asking Grant, 'What's it like? What's the style? What's the boss like? What are the boys like?'
"I was just constantly peppering him with questions. He was just honest with me. Everything he told me was really good.”
Gilmour joined up with Daniel Farke’s side at the start of July and is hoping for regular football to aid his development.
"I had some options but Norwich was first choice,” he revealed. “I came here, spoke to the boss, and everything he said sounded really good; the way he wants to play, the way he sees me fitting in. That was what made my choice easier to come to Norwich.
"Norwich play football that suits my style, playing out from the back and wanting to keep the ball. For me, this was the perfect opportunity. This is my kind of style of play where I want to play out, get on the ball and make things happen.”
Gilmour is eager to get a run of games under his belt with a view to returning to Stamford Bridge an improved player.
"I had to come out and get more experience of first-team football. I need regular football to develop. If I am playing week in and week out I will become stronger, sharper, I will become more aware.”