Shorey, 26, has been linked with West Ham and Newcastle.
Lita, 22, who scored three goals for England in the recent Under-21 European Championships, is reportedly interesting Sunderland and Portsmouth.
"I've held talks with both players' representatives," Reading director of football Nicky Hammond told the club website. "They were very positive."
Shorey has two years left on his current contract while Leroy has one year left on his.
Hammond added: "We're keen to take things forward and the discussions will continue in the not too distant future."
Reading have failed to secure a couple of their planned targets this summer..
"We've missed out on a couple of players that we'd have liked this summer," Hammond told the Reading Evening Post.
"They possibly didn't see Reading as the best possible option they had and we've just got to accept those decisions.
"If we look at what's most important to us, trying to keep our best players is of course top of that list."