Spanish media reports, indicating that a letter of intent may already have been written, said Fernando Alonso favours Australian Webber to replace the struggling Felipe Massa.
The reports also said Webber, 35 and with an expiring Red Bull contract, could be signed for a single season ahead of Sergio Perez joining in 2014.
“Sergio was flavour of the month last week for the Ferrari drive; now it’s me,” Webber said at the Mugello test on Tuesday.
“I’m focusing 100 per cent on this season and doing the best job for myself and Red Bull Racing. I’m not putting any energy into anything else.”
Italian-language reporters also quote Webber as saying: “There’s a whole season ahead of us before we need to think about the future.
“One day the talk is about Jenson (Button joining Ferrari), then it’s Sergio, now it’s me. I haven’t signed anything.”
“My focus is on this team (Red Bull); we’ve had a good start to the season, we’re only four races down and the road is very, very, very long before we start talking about the future.”
As for the closely-contested 2012 championship, Webber added: “The grid is very close together.
“Sebastian (Vettel) had a weekend without problems in Bahrain and won but he didn’t dominate, and that’s the same for everyone.
“No one will be dominant in the first half of the season, so to be third at the start of the European season is not bad,” he said.