Three English clubs weigh up £8m move for Rangers star - reports
Brighton, Southampton and Burnely are all considering a bid for the player, thought to be valued at £8 million.
The right-back has netted 16 goals in all competitions this season - most of them from the penalty spot - and has been an all round attacking force with double digits in assists as well.
Manager Steven Gerrard wants to keep his captain but is braced for bids in the summer transfer window.
Tavernier signed a new contract in September of this season. The deal runs until 2022.