The teenager was introduced to the first-team by previous Stamford Bridge boss Frank Lampard, but has found opportunites harder to come by under the German who took over the reins in January.
Reports in The Sun suggest Gilmour, who began his career at Rangers, could look to make a loan move for regular first-team football – in order to establish himself higher up the pecking order at the Champions League winners later.
He doesn’t have to look far for inspiration and how such moves can work.
Mason Mount, who shares the training centre at Cobham with the midfielder from Ardrossan, spent two seasons away at Vitesse Arnhem in Holland and then on loan at Derby County with his future manager Lampard, before returning to become a fixture for both club and country.
The England international played 39 times in the Eredivisie and Europa League before heading back to England and adding more than 40 appearances for the English Championship side. That in turn led to more than 100 appearances for Chelsea in two seasons and a Champions League winner's medal two weeks ago.
Since moving to London in 2019, Gilmour has played 22 times for the Blues and started each of the five times selected by Tuchel, playing the full 90 minutes against league champions Manchester City last month.
A lack of minutes since the manager's arrival in January had raised concerns over his participation in Euro 2020 but Steve Clarke still selected the youngster, who has impressed in both pre-tournament warm-up internationals.