The centre-back played 38 first-team games for Forest, all but four of them last season.
He has played for England at Under-18, U19 and U20 levels and QPR boss Harry Redknapp is keen to add him to his squad ahead of their Premier League return.
Redknapp – who has already agreed a deal in principal for Rio Ferdinand – is understood to have offered the Championship club in the region of £4million for Lascelles.
Lascelles, who signed a four-year contract with Forest in August 2012, has been linked with other Premier League teams in the past, including Arsenal.
Earlier this year Everton were fined £45,000 by the Football Association for making an unauthorised approach for Lascelles back in 2010.