Horner - one of the most successful principals ever and a leading figure on Netflix's 'Drive to Survive' F1 docu-series - was sacked last May, reportedly with an 80 million pound ($108.72 million) payoff.
Alpine are majority-owned by French carmaker Renault but sold a 24% stake to a group of investors led by Otro Capital in 2023 for 200 million euros ($235.36 million).
Valuations of F1 teams are now considerably higher, with Mercedes recently put at $6 billion.
Otro's group of investors include RedBird Capital Partners and Maximum Effort Investments, with a list of top athletes including Hollywood actors Ryan Reynolds and Rob McElhenney as well as NFL star Patrick Mahomes and golfer Rory McIlroy.
There has been persistent speculation about Alpine and Horner, with the British-based team seen as providing his most likely way back to the paddock as a co-owner rather than employee.
"Otro wants to sell their participation in Alpine," Briatore told reporters at the launch of Alpine's new F1 car on an MSC cruise liner in Barcelona's port when asked about developments.
"It's a few groups interested to buy 24%... the moment somebody buys 24%, we still have 75%, and then we discuss. But for the moment, this is the situation."
Briatore said he had known Horner for many years but that any talks between the Briton and Otro had nothing to do with him or Renault.
"First you need to buy Otro (shareholding), and after Renault needs to accept the buyer," he said. "And after we see what happens."
"But there's no link with me, because he's negotiating with Otro, he's not negotiating with us."
Horner, whose wife is former Spice Girl pop singer Geri Halliwell, is planning to be in Australia ahead of the season-opener in Melbourne on March 8.
The former boss, whose period of 'gardening leave' is believed to run well into the season, has announced stage shows in Sydney, Melbourne and Perth in late February and early March to discuss his career in Formula 1.