An announcement could be made before the end of the week, according to The Guardian, which will see the event return to free-to-air TV.
Sky Sports has lost the rights to the final Major of the year after failing to reach an agreement with the PGA of America, a week before unveiling its new dedicated golf channel as part of a major revamp.
Slumbers has taken a swipe at BBC, however, claiming that the station is "tired and outdated" in a staunch defence of the R&A's past broadcasting decisions.
"We're not uncomfortable at all," he said. "In fact, we are very happy with our partnerships. I think when we moved last year we took what was frankly a fairly tired and outdated broadcast, turned it into absolutely world class and raised the whole level of the way it was shown.
"I think that was a combination and a partnership of those organisations with the R&A that has truly improved how people are watching golf. A testament to that was that [the Open coverage on Sky] won a BAFTA for sport.
"They were up against the BBC's coverage of the Olympics and Paralympics, and also the Six Nations. So I think that was a fantastic testament to what we did last year at Royal Troon, and really shows what you can do with TV. We're building on that this year."
This week's Open Championship will be the second to be aired live on Sky Sports, with last year's tournament suffering a huge decline in audience.