The Hoops boss made a point of praising the 23-year-old utility player 24 hours after he had helped the Parkhead club to their sixth successive Ladbrokes Premiership title win with a 5-0 victory over Hearts at Tynecastle.
Craig Gordon, Kieran Tierney, Scott Brown, Stuart Armstrong, James Forrest and Leigh Griffiths all started in Scotland’s 1-0 World Cup qualifying win over Slovenia at Hampden Park last week.
Rodgers insists McGregor, a former Scotland Under-21 player who has been in the senior squad before but is uncapped, has got what it takes to join them.
He said: “Callum McGregor never gets a mention.
“We have all the stars, all the goals; this was a boy who was absolutely brilliant yesterday.
“I have no question he can play. There is no question about that.
“I want the players to be the very best they can be in their careers. It is a short career for them.
“I have absolutely no doubt that if Gordon is looking for someone who is technically gifted, who can keep the ball, who understands football tactically, a player who never wavers in mentality - he is seven or eight out of 10 every game he plays - who has got Champions League experience, then you wouldn’t go too far wrong with Callum in your squad.”
The former Swansea and Liverpool boss, who reiterated his happiness at being at Celtic by describing it as his “dream job”, elaborated further on his reasons for singling out a player who came through the Parkhead youth system.
He said: “He played in five position for me this season. Wide on the right against Barcelona, centre of midfield, the side of a diamond,has played left-back and is one of those under-rated, under-valued players, but not by myself and the coaching team.
“I had a similar player at Liverpool in Joe Allen and it wasn’t probably until he went to the European Championships (with Wales) and got voted into the team of the tournament that people began to sit up and take a bit of notice of him.
“These guys that are honest guys. They don’t look for glory, they are very efficient, effective in the team.
“Callum has been brilliant for us, a young guy who came through the system.
“He has this unbelievable habit where he rarely gives the ball away and in my teams that is critical.
“Again, lots of players get lots of attention, lots of glory. This guy is a proper young footballer.
“He is vital to this squad. He is clever, he is bright, when the team is stuck he is in the position to receive the ball.
“The courage he has to play football is amazing and what is great for me to see is that progression.”
Strikers Moussa Dembele (hamstring) and Leigh Griffths (back) missed the game against Hearts and will again be out for the visit of Partick Thistle on Wednesday night.