It is understood the League One outfit have been running the rule over the England youth international ahead of a potential loan switch.
Cochrane is well-regarded at the Amex Stadium, having graduated from the club's academy.
His progress was rewarded last summer when he signed a new two-year deal, with the option for an additional 12 months.
The 20-year-old has mainly been limited to age-group football during his time at the Seagulls, scoring two goals in 16 appearances in Premier League 2 this season.
However, he was handed his first-team debut by Graham Potter last September.
That arrived in a 3-1 Carabao Cup defeat to a strong Aston Villa side which featured the likes of Jack Grealish, John McGinn and Conor Hourihane.
He also skippered Brighton's under-21s in Leasing.com Trophy matches on occasions.
Cochrane's talents haven't gone unnoticed at national level, either.
He earned his maiden call-up to the England under-20 squad in November.
He made his debut when replacing Arsenal's Emile Smith Rowe in a 4-0 victory over Portugal, before winning his first full cap in a 3-0 victory against Iceland five days later.
A full season out on loan playing senior football could be the next step for Cochrane's development.
The News understands he is been on Pompey's radar, with head of recruitment Phil Boardman an admirer.
Kenny Jackett has already detailed how he wants to give younger players more of a chance after missing out on League One promotion this season.
As Cochrane is under the age of 21, it would also mean he'd be exempt from the player salary cap that's expected to be put in place for the 2020-21 campaign.
The left-hand side of defence appears an area that will need bolstering during this summer's transfer window.
As things stand, Pompey have no senior option under contract.
The Blues have offered a new deal to Lee Brown and he remains in negotiations.
However, Brandon Haunstrup has turned down fresh terms despite been offered a pay rise.
The Waterlooville lad is closing in on a switch to Scottish Premiership side Kilmarnock.