The Rangers captain has been in inspired form so far this season and Daily Mail claims that the Seagulls could make a move for him in January.
Tavernier was a target for other clubs during the summer but Rangers managed to hold on. Later, the player signed a new contract with the club as well.
It will be interesting to see how Rangers react to any potential offer in January.
Tavernier is irreplaceable right now and selling him would be disastrous for Rangers. Gerrard will not want to lose a key player at any cost.
The report adds that Brighton sent scouts to watch the player in action against Rapid Vienna. Tavernier had a fantastic game during the midweek and the scouts will have been impressed.
The 26-year-old has the quality to make the step up to the Premier League and it will be interesting to see how reacts if a Premier League club comes in for him.
However, a move seems extremely unlikely in January and his suitors will need to wait until the end of the season.