While admitting Championship rivals Forest's high valuation of Antonio is likely to price Leeds out of the market, he is described by the paper as a 'possible option' this summer.
Leeds have acted early to sign four players this summer, including signing Leicester striker Chris Wood for the highest fee they have spent on a single addition in more than a decade.
Owner Massimo Cellino is determined to do all he can to help the club return to the Premier League, and signing Antonio would be a major statement of intent.
Forest would likely aim to resist any advances despite buying the winger for just £1.5 million from Sheffield Wednesday a year ago.
Antonio scored 14 goals in the Championship and 15 in all competitions last season, making him the club's joint highest scorer with Britt Assombalonga, whose season was cut short due to injury.
Forest would therefore be taking a big step backwards were they to sell up, and The Sun reported earlier this year they rebuffed advances from Premier League side West Bromwich Albion.
The ambitious move from Leeds has fans buzzing, even if many are realistic about their prospects of making such an acquisition. Here is a look at how supporters reacted on Twitter...
Michail antonio is the player i wanted us to sign the most, best winger in the league.— luke Hollick (@hollicklufc_) July 3, 2015
Nottingham forest value Antonio at 6m and there's a lot of premier league interest for him, so I think we can forget that. #lufc— ChatLeedsUnited (@ChatLeedsUnited) July 3, 2015