A Ferrari insider, however, insists the story is "not true".
However, it does come amid the latest reports from Britain that indicate Jenson Button's place at McLaren is not secure beyond his existing 2014 contract.
Ron Dennis undoubtedly wants a top driver like Alonso, Sebastian Vettel or Lewis Hamilton to lead the Woking based team into its new works Honda era.
Still, Ferrari insists it is not rushing to tie up the talented Spaniard.
"We have no hurry to renew with Fernando," a team source told the Spanish sports daily AS.
"He has a contract with us until 2016, we are focused on improving the car and nothing else."
According to 1997 world champion Jacques Villeneuve, however, Ferrari should be worried that doors elsewhere are opening for Alonso.
"I think Fernando is tired of working for nothing," the French Canadian told Italy's Omnicorse.
"It shows that he no longer has the joy of driving, as he did two years ago. Then, he carried the team on his shoulders, but last year he gave up.
"He no longer has the strength to drag the team along by himself," Villeneuve added.
But Villeneuve noted that, amid Ferrari's 2014 struggle, there might be light at the end of the tunnel.
"You can see that the work of James Allison is beginning to show," he said, "and that could motivate the driver.
"I think next year we will see a Ferrari in recovery -- if Fernando has the patience to wait for the fruits."