Scottish prospect Gilmour had been on the fringes of first-team action before being trusted to start against Liverpool in an FA Cup fifth-round tie at Stamford Bridge on March 3.
Frank Lampard opted to play the 18-year-old in a central playmaker role, which allowed him to dictate the pace of the game and provide an-all important to link to the Blues’ front three of Olivier Giroud, Willian and Pedro.
With Ross Barkley and Mateo Kovacic working alongside Gilmour, Chelsea were able to dominate in midfield and overpower the runaway Premier League leaders, who were suffering a hangover of sorts after surrendering their unbeaten record against Watford the previous weekend.
Chelsea ran out 2-0 winners on the night thanks to goals from Pedro and Barkley, with Gilmour grabbing most of the headlines for a mature performance which defied his tender age.
Lampard rewarded Gilmour with another starting berth against Everton in the Premier League five days later, and he was again able to play a vital role in a 4-0 home victory.
Gilmour has since been touted for a call up to the international stage, with former Scotland boss McLeish seeing similarities between the teenager and a France legend.
“He reminds me of former France midfielder Alain Giresse, who I remember playing against for Scotland in a warm-up game prior to the European Championships in 1984,” McLeish began.
“Jock Stein came over to me before kick-off and told me to be as physical as I liked against Giresse because, to use that well-worn phrase: ‘He won’t fancy it.’ Famous last words.
“France effectively lined-up with a five-man midfield. Giresse was there – this was that great French side that contained the likes of Jean Tigana and a fella called Michel Platini.
“We were playing a flat back-four and so we had no-one to mark – which was unusual for us – and we were absolutely battered in the first-half. We came in two-down at the break and I still remember Gordon Strachan turning around to me and asking what was the record defeat for a Scotland team against France. We were given a run-around.
“And at the heart of it was this Giresse fella. It didn’t matter how aggressively I went to engage with him, by the time I got there the ball had been moved on. He had an answer for everything.
“The times when I did actually get close, it had no effect. Giresse may have only been small in stature but he was solid.
“And one thing I have picked up on, having watched Billy play for Chelsea and looking back to the time playing for Scotland’s Under-21s, is the fact that they have worked on his core strength.
“The other player he reminds me of – with respect of his willingness to take a ball under pressure in any situation – was Barry Ferguson.
“One of Barry’s many great qualities is that he would accept a pass, regardless of the stadium he was playing in, the opposition or the match situation. He would take the ball and do something positive with it. He would re-cycle it. Take it back, move it forward, sideways – whatever the situation called for, he made the right decision.
“Now, it’s not fair to heap that kind of comparison upon Billy’s shoulders quite just yet but I see the same calmness in possession, like he is one step ahead. It’s a rare quality in the game.
“And if he keeps a level head, he really could go on to be quite a player.”
McLeish added on calls for current Scotland boss Steve Clarke to include Gilmour in his next squad: “Now, of course, there will be a clamour for Steve to include him. And he does have a difficult choice to make in there because he already has good midfielders.
“More importantly, he has established some momentum in that area of the field and he won’t want to disrupt it.
“The likes of Ryan Christie and James Forrest for instance, aren’t going to give up their places lightly.
“But at the same time, if Billy is playing regularly for Chelsea, then it is very difficult to ignore him. Steve knows only too well the level and quality that is demanded at Stamford Bridge.
“The point is, if Billy is progressing and playing then he is going to get a look in sooner rather than later. And if he can take that step up in his stride in the way he has taken to the Premier League, then he could take some dislodging.”