Martinez's departure from Goodison Park is said to be imminent.
Toffees boss Martinez is under mounting pressure after leading the club to one league win in their last ten attempts and a report in the Daily Mail on Thursday claimed the Spaniard's apparent no-show at training has left players anticipating his departure.
However, Irvine is unsure whether Everton chairman Bill Kenwright will break with tradition and dispose of Martinez, the third manager of his 16-and-a-half-year reign.
"It’s a very difficult situation for Everton," the Scot told the Alan Brazil Sports Breakfast show on Thursday. "It’s a club that sticks with its managers so I’m not necessarily thinking Roberto’s going to lose his job just now. Bill and the new owners might think: 'Let’s keep him on.'"
However, with Iranian billionaire Farhad Moshiri acquiring a majority stake in Everton earlier this year, Irvine added: "I’ve always felt they’re in steady hands with Bill, and I’m a little bit unsure how the club will react now at this time with the influence of the new investor."
Irvine, who is currently the assistant manager of Championship side Blackburn Rovers, has coached in separate spells at Goodison Park.
The 58-year-old was assistant manager during David Moyes' reign, and returned to the club in 2011 as academy boss, where he later worked under Martinez.
He left to take control of West Bromwich Albion two summers ago, but was sacked six months into his tenure.