The youngster, who has represented Portugal at Under-21 level, has impressed since his debut at the beginning of last season, reportedly catching the eye of La Liga giants Real Madrid and Barcelona.
However, it is believed that Blues boss Jose Mourinho is prepared to steal a march on his rivals by making a bid as early as January.
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Chelsea's vulnerable midfield has been heavily criticised this season following the west London outfit's start of just four points from five games, with Cesc Fabregas' defensive commitment questioned, while Nemanja Matic has failed to impress after last season's stunning performances.
Neves would offer Chelsea a dynamic shield for their defence in a similar style to Matic - his priorities lie in protecting the back line whilst equally comfortable with the ball at his feet, prompting attacks.
Despite his tender age, Neves has established himself as a regular at the Estadio de Dragao, displaying incredible maturity, which could stake an immediate claim to a position in the Blues' midfield should he make the move.
He would also add some youthful vigour to a side that has looked laboured this season, and help Mourinho to build his "dynasty" at Stamford Bridge.
Porto are likely to be resistant to relinquish their rising star, who has emerged from their own academy, but have shown in the past that their stars have a price - Jackson Martinez, Danilo, Juan Iturbe, Eliaquim Mangala and James Rodriguez have all been sold by the Portuguese club in recent seasons.
Jose Mourinho will also be hoping to exploit his links with his former club, where he is still viewed favourably following his unlikely Champions League triumph in 2004.
Chelsea had previously been linked with a move for Juventus superstar Paul Pogba, but Neves may be able to offer a more affordable and attainable alternative. It is also unlikely that Juve would be willing to sell mid-season.