Dickov led the npower League One strugglers to an improbable FA Cup fourth-round victory over Liverpool yesterday but was forced to field questions surrounding his future after the match.
Corney's refusal to back his manager in the immediate aftermath of the 3-2 Boundary Park triumph fuelled speculation that the former Scotland international would ultimately pay the price for a run of seven defeats and one draw from the Latics' last eight league matches.
But Dickov, who saw three key members of his backroom staff placed on gardening leave on New Year's Eve, has earned a reprieve and is set to lead Oldham for their trip to Walsall this weekend.
Dickov told Sky Sports News: "I've been with Simon this morning and Simon's told me that he wants me to stay on.
"He's obviously said that decision's up to me ultimately, and I'll just carry on as I did do last week and the week before, and last season and the season before that.
"I'm happy to carry on, I love my job. I'm a lucky boy to have a job, there's only 92 of us in the league and I just want to be the best I can.
"I'll work as hard as I can and if I do that we've got a chance of winning games."
Winning games in the build-up to next month's mouth-watering fifth-round meeting with Everton appears vital to Dickov's prospects of being in the dugout for the tie after Corney failed to offer firm assurances on his position.
Despite enjoying a triumph that harked back to the club's halcyon days under Joe Royle two decades ago, the New York-based businessman insists survival in the third tier is paramount and believe Oldham's current slump in the league makes it understandable that Dickov's position should come under scrutiny.
"I don't think (Dickov departing) is inconceivable," Corney said. "I think Nigel Adkins leaving Southampton was inconceivable because he hadn't lost in five games.
"We've got one point out of 24 and football is a results-driven business.
"We need to win games, we need to stay in this division and you have to make decisions.
"Sometimes they're very, very tough. I've never had any enjoyment when I've fired the manager, I'm friends with all the ones we've parted company with.
"I don't want to lose Paul but there comes a point, whether it's Man United, Man City - whoever it is, you're going to find yourself in a situation one day when you need to make changes."
Dickov's quest for crucial points in the coming weeks may take place without some key members of his squad after yesterday's famous win came at a cost.
Youssouf M'Changama provided the left-wing cross for towering striker Matt Smith to give the Latics an early lead, but he was soon forced out of the action by a late challenge from Raheem Sterling which saw the Liverpool winger booked.
The midfielder faces a scan on his knee to discover the extent of medial knee ligament damage.
Smith's all-action two-goal display was cut short when he sustained a shoulder injury in the closing stages and Oldham's medical staff are awaiting the results of an x-ray, while strike partner Robbie Simpson picked up a hamstring problem.