Manchester City, who take on Southampton this afternoon, are 10 points behind the Reds in the Premier League title race.
They only brought in Riyad Mahrez in the summer while Liverpool splashed cash on the likes of Alisson, Naby Keita and Fabinho.
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But McGarry thinks the way Jurgen Klopp’s men have taken the league by storm will spark City into action.
And he says defensive midfielder Thomas Partey, the 25-year-old Ghana international, is on their wish-list.
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McGarry told the Transfer Window podcast: “I’m told that City have enquired to Atletico Madrid about Thomas Partey.
“For me, he is one of the most exciting and most effective holding midfielders in European football at this moment in time.
“He would be my choice for Pep Guardiola in terms of bringing someone in going forward.
“Remember that City were very much in the market for Fred, the Brazilian midfielder who signed for Manchester United in the summer, so this is not a position which Guardiola is just suddenly waking up to in terms of it being deficient.
“He’s been looking at this for a year now or more and unusually City have not really responded or reacted properly to this.
“However, I do believe that the losses to Crystal Palace, Leicester City and Chelsea, and the fact they’re trailing Liverpool and Tottenham Hotspur in the Premier League, means that they will act and act quickly in January.”
Partey was nominated for the BBC African Footballer of the Year award earlier this month.
However, he was beaten to the honour by Mo Salah who lifted the crown for the second year in a row.