Warburton captained the Lions in the first two Tests of their victorious tour of Australia in 2013 with Jones deputising for his injured Welsh teammate in the triumphant final test.
And with the Wales team boasting a number of experienced leaders, Warburton is not sure if he will be the man to lead for Warren Gatland once more.
"Outside of campaigns nobody knows who the Welsh captain is and nobody assumes," Warburton told Wales Online.
"I have not been Welsh captain for six months. Somebody might introduce me as the Welsh captain but technically I am not.
"We have a lot of leaders now if you just look at the likes of Alun Wyn Jones, Dan Lydiate, Gethin Jenkins, Jonathan Davies, Dan Biggar and Jamie Roberts among others.
"If I turned up for a Welsh squad I would never be concerned about players not wanting to influence training or the game."