The News understands that the Blues have been keeping tabs on the left-back ahead of a potential summer move to Fratton Park.
Vincent has come through the youth ranks at the Ravens after joining the club at under-14 level.
Having signed first-team forms at Hayes Lane last September, the 18-year-old has featured seven times during Bromley s National League promotion push this season.
Vincent made his debut off the bench in a 2-0 win over King's Lynn in February before being handed his maiden start in a 2-2 draw with Wealdstone last month.
Vincent also delivered an impressive performance in Bromley under-18s' shock 2-1 win over Pompey in the FA Youth Cup at Fratton Park in December.
He bagged the visitors' equaliser in the first half before sending in the corner that led to Ben Krauhaus’ winner.
As things stand, Lee Brown is the only specialist left-back tied down heading into the 2021-22 campaign.
Charlie Daniels’ deal expires in June while youngster Harvey Rew has been informed he’s being released.
Should Vincent earn a switch to PO4, he will be the third player to move to Pompey from Bromley in four years.
Louis Dennis was recruited in the summer of 2018 on a free transfer.
Meanwhile, the Blues purchased Reeco Hackett-Fairchild for an undisclosed fee in January 2020.
The forward has played just once for Pompey so far and spent this term on loan at his former club and before moving to Southend United in January.