West Brom boss Alan Irvine has admitted he is keen to add another striker this summer after already signing Brown Ideye.
Swansea boss Garry Monk is adamant that only an “astronomical” bid could prise Wilfried Bony away from the club.
O'Neill's original two-year deal expires at the end of December and, although he has won just one of his 14 matches at the helm, he has the support of key officials at Windsor Avenue.
Talks have been ongoing for a number of weeks and though nothing has yet been signed, Press Association Sport understands that both parties are keen to finalise terms for another two years.
O'Neill, who managed Shamrock Rovers before taking over from Nigel Worthington, has had an up and down stint in charge of the national side with a memorable win over Fabio Capello's Russia and a brave draw away to Portugal tempered by defeats in Azerbaijan and Luxembourg.
Northern Ireland finished fifth in their World Cup qualifying group with seven points.
O'Neill has a chance to add a second win to his CV on November 15 when his side travel to Turkey for a friendly.
He announces his squad on Tuesday.