Phil Neville admits it is flattering to be linked with the manager's job at Everton and believes he has the experience.
Samir Nasri has backed the potential arrival of Manuel Pellegrini as the new boss at Manchester City.
Jones, who took over at Hillsborough in March, watched the Owls slump to a seventh straight league defeat but the former Cardiff boss remains defiant.
"Pass the problem onto someone else? I'm a bigger person than that," he told BBC Radio Sheffield. "If a decision is made I can't have any choice in that, but I've never walked away from anything in my life.
"Everybody always wants you to walk away in football. It's a sad indictment that somebody who comes to the game thinks you should lose your job because things aren't going well.
"Where's the sticking together? The fighting through it? Where's that attitude?"
Chairman Milan Mandaric recently handed Jones a vote of confidence with the majority of those defeats coming at the hands of sides in the promotion mix.
But Saturday's defeat marked their first against one of the clubs in the bottom four with a Yorkshire derby coming against fellow strugglers Barnsley next weekend.
"We know we have to get results. I know how the football world works. We've had 12 managers in 15 years which is a lot and we're still where we are," Jones added.
"You've got to have time. Six months in we got promotion, and all of a sudden it's 'he's not got this' or 'not got that'
"Most of my career has been at the top end, but when you're down at the bottom, it doesn't mean your values and way of going about things is wrong - it's the only job in the world where people think they can do a better job."