Manuel Pellegrini is a big admirer of the Sporting Lisbon starlet - who has attracted interest from United - and has been quoted a 38 million-euro fee for the midfielder.
City has scouted the powerful 21-year-old defensive midfielder on several occasions in the last month and is aware of United having registered official interest in the player.
It is City’s understanding that the Portugal international has no firm preference in terms of his next club but is keen to move to a side playing Champions League football next season.
Manuel Pellegrini is a keen admirer of Carvalho, who made his full international debut in last year’s World Cup playoff against Sweden, while City’s director of football Txiki Begiristain has been told the player would be available for a fee of 38 million euros.
The player himself has admitted to being flattered by the interest of United, which Goal understands will have around 180 million pounds to spend on squad reinforcements in the summer.
Speaking after Sporting’s 2-1 win over Braga earlier this month, Carvalho said: “It’s nice being praised and to know there are some big clubs interested in me.
“[My future could be with] Manchester United or Real Madrid. It’s just nice to have a great European club after me, but at the moment I’m just totally focused on Sporting and doing my best until the end of the season. At the end of the campaign, we will see what happens.”
City is focusing much of its transfer activity on Portuguese-based talent and maintains an interest in Porto pair Eliaquim Mangala and Fernando.
Although currently well stocked for midfield options, City is expected to lose Gareth Barry at the end of the season, who could make his move to Everton a permanent one, while Jack Rodwell is also likely to be made available.