Harris was released by Cardiff City after a difficult season in the Premier League.
Harris only started three games, with 10 substitute appearances, scoring once.
The previous season in the Championship he scored four goals and provided four assists, and Sheffield Wednesday believe he will be a strong addition to their team.
Earlier this season The Sun claimed Leeds United were keen on a move for the winger.
Now he is available for free, the Whites may be missing out on a real bargain, especially considering their lack of wingers in the squad.
Leeds are at risk of losing young talent Jack Clarke, with Tottenham interested, The Mirror report.
BBC Sport report Leeds want a loan deal for Wolves winger Helder Costa, but Harris is a player Leeds could get in on a permanent.
Harris earned the praise of Cardiff's Neil Warnock earlier in the season, telling BBC Sport: "He's been the best player in training for the last six weeks, he's been an absolute breath of fresh air for me as a manager."
There is plenty of time this transfer window for Leeds to pick up other targets, but as next season goes on, they could end up regretting not taking a low risk punt on the 26-year-old.
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