O'Neill, who takes charge of his final contracted match against Israel on Tuesday, has been involved in tentative negotiations with the board but pressure on him has increased following disappointing defeats to Luxembourg and Azerbaijan in World Cup qualifying.
Some fans have started to question if he is the right man to take the side forward, despite repeated warnings that he is overseeing a period of transition for the side.
But Shaw does not share that uncertainty.
"We have started the process and it will go on through October and possibly beyond," he told the Belfast Telegraph.
"I personally haven't changed my view and still want Michael to continue and believe he remains the right man for the job."
O'Neill is popular among the squad and has the backing of senior players, but a record of one win in 13 is a poor verdict on his time so far, despite promising results against top opposition such as Russia and Portugal.
Source: PA
Source: PA