The Jamaica international winger signed a three-year deal when he joined the Royals from Nottingham Forest in May 2012.
He made 42 appearances in the Sky Bet Championship last season, scoring five goals, as Nigel Adkins' side narrowly missed out on a play-off spot.
McCleary, who turned 27 last week, could now be set for a Premier League return this summer. Steve Bruce's Tigers and Garry Monk's Swans are keeping tabs on the player, according to Sky sources, while Crystal Palace are also understood to be interested.
Relegated duo Norwich and Cardiff may also be in the frame for his services, should Reading decide to sell him.