The 44-year-old's current deal is due to expire following Tuesday's final World Cup qualifier against Israel in Tel Aviv.
However, Shaw is confident that O'Neill will sign fresh terms with the national team once the qualifying campaign is over.
"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 took charge of Northern Ireland in December 2011 when he replaced Nigel Worthington.