Leafs have inquired into Barrie for years as he has been available dating back years.
Here was a great article from 2016 and analyzing Barrie.
Tyson Barrie has some of the worst Corsi numbers in the NHL
Three years into his career, Tyson Barrie is top of the list of trade rumours. But he is challenging for bottom of the list in Corsi. Is that a measure of the man or the team? Is this a deal the Leafs should try to make? On May 13,2016 Elliotte Friedman told the Edmonton radio audience that he thinks the Colorado Avalanche are trying to trade Tyson Barrie. Friedman, whose rumours often prove to be very true......
"The eye test
Barrie is not like other defencemen in how he plays. His approach to the game makes the Karlsson comparison slightly more valid, but he is even more of a puck handling, shooting, fourth forward than Karlsson is.
I've seen seasoned commentators flummoxed by watching him repeatedly be the first man into the offensive zone with the forwards trailing well behind. Not just the guy who carries the puck across and passes it off, the guy who drives the net like he's the star center on a breakaway".
If you like analytics then this is a good read for you.
Link:
Tyson Barrie has some of the worst Corsi numbers in the NHL