Analysts have said that Diageo is best placed to buy Jose Cuervo, the world's best-selling tequila, if the Beckmann family decides to sell the brand which could fetch $2 billion.
The Sunday Times said the two sides had held a series of discussions about a sale and that the Beckmanns wanted shares in the British group rather than cash.
Diageo, the world's biggest spirits group, would be front runner to buy Jose Cuervo due to its existing distribution rights and strong balance sheet and Chief Executive Paul Walsh has said in the past he would be interested in buying at the right price.
The newspaper said the sale for shares deal was one of several options being considered by the Beckmanns who are thought to value the business at between $3 billion and $5 billion.
Diageo has a market value of just over $50 billion.