Leeds were one of the first English clubs to be credited with interest in Cochrane, who has impressed in his first senior campaign - despite having only turned 16 last April.
And it is claimed that Everton, who have recruited a number of talented British youngsters over the past couple of years, could even make a move for Cochrane before the end of the January transfer window, having moved ahead of the chasing pack.
However, with a string of players already on Everton's books in Cochrane's position, it is likely the Glaswegian would stand a better chance of securing immediate first team football at Leeds.
Cochrane was on the books of Glasgow Rangers before moving to Hearts four years ago.
Would Cochrane be a good signing for Everton?