Young is wanted by Tottenham and his possible departure was thought to be a factor in Martin O'Neill's resignation as Villa boss earlier this week.
But sources close to the 25-year-old have suggested that after "positive" discussions, he is now likely to stay.
Spurs manager Harry Redknapp is a long-term admirer of Young, and keen on signing him.
But Villa are believed to have made it clear they want to keep him, and the player's wage demands are also a stumbling block to any move.
For Spurs to capture Young, they would have to break their strict wage structure - something chairman Daniel Levy is reluctant to do.
Young, who played for England in the 2-1 victory against Hungary on Wednesday, has less than two years left on his Villa contract.
O'Neill had already admitted defeat in the bid to prevent James Milner moving to Manchester City, saying last week: "Losing your best players at the club obviously causes you a headache and it is a problem. "
Source: BBC Sport
Source: BBC Sport