Since taking over from Mick McCarthy, Connor has seen the Black Country club slide further towards the drop and they are now nine points adrift of safety.
"I'm a big boy," said the 49-year-old. "I know the score in football. I know what happens if Wolves are relegated. I went in with my eyes open.
"I'm sure I could swallow my pride and do something else."
Connor, who has been with the club for 13 years, added: "It is kind of strange when people say your future rests on 13 games after 13 years here. I knew when I took over that would be the case and I welcome the challenge."
He has collected just one point in his eight games in charge of the club.