Queens Park Rangers are apparently interested in selling Luongo with his contract expiring in 12 months time.
The 26-year-old has been with the West London club since 2015, but London Football News reports both Forest and Leeds are "considering a move for Luongo".
The Sydney-born central midfielder has established himself as a regular in the Championship, with 154 appearancesm 10 goals and 16 assists since joining QPR.
Should Luongo join up with Leeds, his very first game for the club could be in Australia.
Marcelo Bielsa's men will take on Manchester United on July 17 in Perth and then Western Sydney Wanderers on July 20 in Parramatta.
Meanwhile, Forest are looking to build on their ninth-placed finish last season as they push for promotion to the Premier League.
