After graduating from the Brighton & Hove Albion academy in August 2019, the 23-year-old enjoyed loan spells at Union SG in Belgium and Tynecastle before moving to Scotland permanently ahead of the 2022-23 season.
Cochrane has been a regular figure for the Jambos at left-back this season, making 23 starts in the Scottish Premiership, providing three assists.
The defender also possesses some international experience, having represented England Under-20s during the earlier stages of his blossoming career.
According to Edinburgh News, Hearts have decided on a transfer strategy as the club looks set to receive offers for Cochrane during the upcoming summer window.
The report claims that Steven Naismith's side have slapped a £2m asking price on the former Brighton man, with interest from English clubs expected.
It is understood that Hearts will be firm in their negotiations, with the aforementioned seven-figure sum being the minimum that they will agree to ahead of next season.
Following supposed interest in Cochrane during the January transfer window, it is said that Vincent Kompany's Burnley could be back in the race when trading resumes in the summer.
The Clarets' Lancashire rivals Blackburn Rovers were also linked with a move for the left-back, however a potential summer swoop is likely dependent on their divisional status come August.
Having failed to win any of their eight league matches since John Eustace arrived to replace Jon Dahl Tomasson at Ewood Park, Rovers are sitting in 17th in the Championship standings, three points above 22nd-placed Huddersfield Town.
It is also believed that fellow second-tier outfit Ipswich Town have been monitoring the progress of Cochrane, who is preparing for a switch away from Tynecastle in the summer.
Looking towards the future without the 23-year-old, Hearts have reportedly agreed to sign left-sided defender James Penrice from Livingston in the summer.
With the Livi Lions currently 10 points adrift at the foot of the Scottish Premiership table, 25-year-old Penrice is set to secure his status as a first-tier footballer by switching to the Edinburgh club.
Also planning for the long term, Burnley's interest in Cochrane is further legitimised by the situation of Clarets left-back Charlie Taylor, who is fast approaching the end of his deal at Turf Moor.
Despite making over 20 Premier League appearances this term, the former Leeds United man is currently unsure whether he will extend his stay in Lancashire past the conclusion of the season.