The club are forward planning for his potential departure after the 4-0 loss to Everton, which followed the 4-2 defeat to Bournemouth.
But O'Neil, speaking defiantly in his pre-match press conference before Monday's trip to West Ham, was adamant he is focusing on preparing the team after taking training on Thursday morning.
He said: “I don't think about me personally, I think about the team and where we are in the league, and the last two results let us down from the momentum that we created.
“But there always comes the next challenge, which comes very, very quickly at West Ham on Monday.
“There's a lot in the last two games that the group needs to take on board and learn very quickly from if we want to have a chance of being more competitive, more consistently.