It follows Saturday's loss to South Africa.
Reports suggest Warren Gatland is the favourite to lead the British and Irish Lions again in 2025.
The Kiwi - who has been head coach for the last three tours - was also involved as forwards coach in 2009.
South Africa won this summer's series decider by 19 points to 16 on Saturday.
The Lions visit Australia in four years' time.

Thursday Morning Sports Update
Former Liverpool And Blackburn Full-Back Inge Bjornebye Joins Rangers As Football Consultant And Advisor
Lizzy Kent Appointed FAI's New Head Of Women And Girls Football
No Afternoon Session At The PDC World Darts Championship Today
Wednesday Morning Sports Update
Tuesday Morning Sports Update
Niall Kelly Retires From Inter County Football
Boxing Promoter Frank Warren Revealed Potential Fight Between Anthony Joshua And Tyson Fury