Tavernier has impressed in the five games he has played for Gateshead.
Tavernier, who can also play at centre-half, is also expected to extend his stay with Blue Square Bet Premier outfit Gateshead.
Manager lan Bogie: "Keeping Tavernier at Gateshead on a temporary basis will be a big plus as he has done very well.
“He is a talented players who is comfortable on the ball and has good pace, and he has fitted in well."