The 17-year-old moved to Chelsea FC from Scottish side Rangers in the summer of 2017 and he has been gradually getting used to life at the west London club.
Gilmour made a string of impressive performances for Chelsea FC’s youth teams last season and he was invited to train with the first team at Cobham at certain points.
And the teenager has conceded that getting the chance to train with some of Chelsea FC’s top first-team stars was a surreal experience.
Speaking in an interview with BBC Scotland, Gilmour said: “It was a good experience. I went round there with the other two boys.
“You’re out on the training pitch and you start to see Hazard coming out, Fabregas and then Giroud and you’re thinking, ‘Jeez oh, you play with them on Fifa!’
“But no, the standard was amazing. Just to get up close to them and watch what they do, it’s unbelievable.
“Sometimes you could break under that (pressure). But I was just loving it. Getting on the ball and doing your stuff in the training sessions, then you’re passing to Hazard, hitting a shot into Courtois – that’s dreams!”
Meanwhile, Chelsea FC are currently getting used to life under new manager Maurizio Sarri after his appointment as Antonio Conte’s successor at Stamford Bridge.
The Blues have made a solid start to the new campaign and have won all four of their opening four Premier League games.
Chelsea FC will return to Premier League action after the international break when they take on Cardiff City.
The west London side are aiming to challenge for the title after having finished fifth under Antonio Conte last term.
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