The 24-year-old attacking midfielder passed a medical at Madejski Stadium this week and is now in contract talks with the club.
Oxford-born McCleary was voted Forest's Player of the Year but his contract is due to expire next month when he will become a free agent.
Forest are eager to keep him at the City Ground, but the lure of the Premier League and the wages that come with it will tempt him away.
McCleary had an impressive season for Forest scoring nine goals, including a four-timer in their 7-3 victory at Leeds United.
Royals boss Brian McDermott has been tracking the tricky winger for months.
McCleary spent two seasons at McDermott's first managerial club Slough Town in 2005-07, scoring nine goals in 42 games.
Meanwhile, McDermott is still interested in signing Huddersfield Town hotshot Jordan Rhodes.
The Chronicle revealed Reading's interest in the 22-year-old striker back in January.
The Terriers were reluctant to sell at that point but may be willing to cash-in this summer.
Rhodes, with 38 goals in 43 games this season, could cost around £6 million and Reading are likely to face competition from a string of rival clubs.
McDermott is due to watch Rhodes in action tomorrow when Huddersfield take on MK Dons in the League One play-off semi-finals.
He will also cast his eye over Reading defender Sean Morrison who is on loan at Huddersfield.
Valenciennes midfielder Carlos Sanchez and Newcastle's out-of-contract Danny Guthrie have also been linked with the Royals.