Then Reds manager Dalglish had worn it. So too had Ian Callaghan and Kevin Keegan, celebrated players dear to Anfield hearts.
It was 12 January 1991, and Carter had only signed for the reigning English champions from Millwall two days earlier. The winger, aged 25, was about to make his debut. But there was something many did not, and still do not, know about him: he was a player with Indian heritage.
“That was probably one of the best moments in my life and one of those moments I’d dreamed of as a kid,” says Carter of being handed the shirt.
“I looked at the back of the shirt, I looked around a little bit – a few of the players are watching with a few little smiles. You can imagine, every single one in that Liverpool dressing room was an international.
“To think that Kenny had just come up and given me that seven shirt – this skinny little Indian boy who grew up in Stoke Newington. It does not get any better than that. Incredible.”
Carter’s move to Liverpool did not work out. Dalglish left soon afterwards and his successor, Graeme Souness, deemed him surplus to requirements.
He left to join Arsenal and, when he made his debut for the Gunners in August 1992, became the first British Asian to play in the Premier League. It would take 11 years for another to follow in his footsteps.
In an English game where players from that background are conspicuous only by their absence, none of the handful of the British Asian players since Carter have scaled the kind of heights he rose to in playing for such illustrious clubs.
Now aged 55, Carter admits his Indian background still comes as a “shock” to many when they learn of it and, because of his surname and light skin tone, “no-one really identified” him as being of Asian origin during his career.
“I think they just saw a guy running up and down the wing, thinking: ‘He doesn’t mind the odd sunbed or two,'” he says.
The truth is, he was much more than that.
Carter explains that his surname dates back to an English ancestor from the 17th Century who, after moving from London to India, married an Indian woman and settled in the country.
His father, Maurice, was born to Indian parents in Kanpur and brought up in Lucknow in the north of India, where he attended La Martiniere College, a prestigious private school established in 1845 under colonial rule.
Maurice was orphaned at the age of 14 and, left “lost” with “no family to speak of”, joined the Indian merchant navy when he was 16.
“He sailed the seas and loved his sport,” Carter says fondly. “He was a boxer in the navy and turned out to be one of their leading boxers of all time. He had 38 fights and never lost one.”
Maurice eventually came to England and married an English woman but, after having two boys, the pair divorced. Maurice took custody and brought his sons up in Hackney, east London, “essentially as Indian kids”.