Mooy joined Brighton on a season-long loan from Championship side Huddersfield Town in August 2019.
After impressing in a series of appearances, including man-of-the-match performances against Arsenal and Bournemouth, Brighton is keen to lock down the Australian playmaker, according to .
"Mooy has been the subject of interest from a broad range of Premier League clubs but his only match of the season for Huddersfield, in a defeat to Derby, means he cannot play for a third club in one season due to Fifa rules," writes Mike McGrath.
"According to sources at the John Smith's Stadium, Brighton have moved swiftly to make sure they land the former Manchester City player rather than be involved in a bidding war at the end of the season."
Huddersfield are reportedly keen to cash in on the former A-League star, as they look to re-invest in their struggling squad.
Brighton currently sit in 15th position in the Premier League, just two points above the relegation zone.
Mooy would be the club's first 'signing' of the January transfer window, in a deal worth a reported £5 million ($9.6M AUD).