The Guardian Media Group said in a statement that it is in talks to offload the weekly publication for an undisclosed amount to Tortoise Media, launched in 2019.
GMG added that a sale would see The Guardian, its flagship title, remain a 24/7 online offering but with greater global reach and funding by its readers.
"The Guardian's parent company has announced that it is in formal negotiations with Tortoise Media over the potential sale of The Observer, the world's oldest Sunday newspaper," a statement said Tuesday.
GMG said the offer "was significant enough to look at in more detail".
GMG chief executive Anna Bateson said a sale "provides a chance to build The Observer's future position with a significant investment and allow The Guardian to focus on its growth strategy to be more global, more digital and more reader-funded".
Founded in 1791, The Observer was bought by GMG in 1993.
"Since then it has coexisted with the Guardian, which will remain a seven-day-a-week digital operation regardless of the outcome of the negotiations," the parent group added Tuesday.