The 18-year-old Portuguese was a key part of the Porto side that beat the Blues 2-1 in the Champions League on Tuesday.
According to Simon Johnson in the Evening Standard, Chelsea are now lining up a summer bid of £29 million to bring the youngster to Stamford Bridge.
Per Johnson, while Frenchman Pogba remains the west London outfit's No. 1 target, they fear he has decided to join Barcelona at the end of the 2015-16 season.
Neves is undoubtedly an able alternative target, and he would add much-needed depth to the centre of Chelsea's midfield.
Blues boss Jose Mourinho is currently overreliant on Nemanja Matic and Cesc Fabregas in the middle of the park.
Such a scenario was fine last season as the pair performed and Chelsea won the Premier League.
However, Matic and Fabregas have both been poor so far this season—along with various others—and are partly responsible for Chelsea's current lowly position in the English top flight, per SB Nation's Graham MacAree:
Neves would provide an alternative option in midfield and could become a genuine superstar under Mourinho's tutelage.
He has been favourably compared to Barcelona enforcer Sergio Busquets by team-mate Cristian Tello, and he is only going to improve with greater experience, per Portista (via ESPN FC's Nick Dorrington).
Chelsea failed to strengthen adequately in the recent summer transfer window, and they are paying the price, with Bleacher Report's Andy Brassell predicting yet more misery when the Blues face Southampton this weekend:
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It is clear that they need to add reinforcements in the near future and refresh the spine of the side—Chelsea bastions like Didier Drogba, Frank Lampard and Petr Cech have all recently departed the club.
Neves would be a fantastic addition to Mourinho's squad and a potential bargain at £29 million as he could become a Chelsea stalwart for the next decade.