Sven-Goran Eriksson was shown the door by the npower Championship outfit on Monday night after a year in charge, with the Foxes having won just five games this season despite being only two points off the play-off places.
When asked if he intended to approach O'Neill about the position, Raksriaksorn told Sky Sports News: "I don't want to say that because I have to open my mind now, not just what the news or the fans want."
Leicester have been strongly linked with a move for former boss O'Neill, who twice led City to League Cup glory in 1997 and 2000, as well as promotion to the Barclays Premier League and a subsequent successful stint in the top flight.
Raksriaksorn added: "I have to listen to everyone and make a decision very carefully.
"The next manager should be taking us to the Premier League and I think he has to know this league because it's very tough, very tight."
O'Neill, who has been out of work since parting ways with Aston Villa last summer, is firm favourite with bookmakers for the vacancy, with Mark Hughes also a frontrunner.
However, Leeds manager Simon Grayson and Huddersfield boss Lee Clark have both dismissed speculation linking themselves with the job.
Meanwhile, Raksriaksorn revealed he was upset at Eriksson's departure earlier this week.
He added: "Sven is a good man, a very, very nice man and actually I am sad, but life has to move on. I think he had to move on."
Source: PA
Source: PA