Steve Clarke is due to name the 26-man squad he is taking to the tournament on Wednesday afternoon and McCoist has tipped three young players to be part of the Scottish training base in Middlesbrough.
The former Rangers manager believes PFA Scotland young player of the year David Turnbull deserves a call-up, as does Nathan Patterson of Rangers.
And McCoist also says Kenny McLean’s injury leaves a central midfield berth for Chelsea midfielder Gilmour who has yet to be capped for the senior national team.
“Patterson has come in and shown that he’s very comfortable at that level and some of his European performances have been good. Turnbull has been arguably Celtic’s best player - I think he’s had a tremendous season,” McCoist told Sky Sports.
“And Billy Gilmour I think you’ve got to give him an opportunity. I know he’s not had a lot of game time but I saw him in the Manchester City game and he looked excellent - if you can play in that company you can play with anybody.
“We have sadly lost one of our key players in Kenny McLean - a savage blow for him – and sadly for him one door closes and another on opens.
“It is the strongest area of the team and I think if Billy Gilmour was on the periphery then Kenny McLean’s injury gives him a better chance - and I would take the chance and put him in the squad.”