The German car company and its F1 team boss Toto Wolff had agreed in principle with Alpine owners Renault to buy the 24 per cent stake in their team that is owned by investment group Otro Capital.
But the BBC, citing "insiders", said Otro wanted a price Mercedes thought above market value, prompting the deal to collapse.
The BBC reported Otro wanted $720 million (£536 million) for its shareholding, a figure that values the team at $3 billion (£2.2 billion).
Otro paid 200 million euros (£171 million) for its stake in June 2023.
A source at Renault told the BBC: "We understand that discussions have stopped."
Mercedes and Wolff have yet to comment.
Other recent deals involving Formula One team ownership have seen Mercedes valued at £4.6 billion and world champions McLaren at £3.5 billion.
Both of those teams, however, are profitable, and vastly more successful than Alpine, which is fifth in the constructors' championship after five races this season, having finished last in 2025.
Mercedes are set to reduce their number of customer teams in F1 to two ahead of new engine regulations that are due to come into force by 2031 at the latest.
They currently supply McLaren, Williams and Alpine.
Williams are Mercedes' longest-standing customers, followed by McLaren, with Alpine only coming on board this year.