The 21-year-old centre-back is reportedly wanted by manager Roberto Mancini to act as one of the players available for cover if first-choice centre halves Kolo Toure or Joleon Lescott are unavailable for any reason.
Carrico graduated out of the Portuguese club's youth academy in 2007, and spent a split season on loan with Olhanense and AEL Limassol before returning to his mother club in 2008.
He has since established himself as an integral part of the Lisbon-based outfit, and is believed to have attracted potential suitors with his stellar performances.
The young defender has also represented Portugal at Under-19 and Under-21 levels, and it is said that City have had their eye on the budding talent for some time now.
Spanish clubs Atletico Madrid and Valencia are also believed to be in the running to secure the player's services.
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Player Ratings: AC Milan 4-0 Arsenal
Goals from Kevin-Prince Boateng, Robinho and Zlatan Ibrahimovic handed the Italian side a victory that all but seals their progression to the next round of the Champions League
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Ajax - Manchester United Preview: Nani, Jones & Smalling return
The 38-year-old former Wales international was involved in the Red Devils' last second tier European match as they crashed out to Russian side Rotor Volgograd in 1995
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Porto - Manchester City Preview: Europa League holders yet to taste defeat at home this season
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Word on the Tweet: Rooney names his new horse after himself
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Should Copa America 'Vanishing Spray' be introduced globally?
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