Tim Lincecum told the San Francisco Chronicle in September that he was comfortable going year to year with his contract.

The Giants, who control Lincecum for two more years, want to sign him long-term.

The solution?

It might be one extreme or the other.

Lincecum, coming off a two-year, $23 million contract, said he would be comfortable on a one- or two-year contract.

The Giants might need to make him a monster offer – one of say, six to eight years – to persuade him to sign a longer deal.

“It depends on how they come after me,” Lincecum told the Chronicle. “If it’s aggressive, obviously I want to take that into consideration and talk about it with my agent and see what he thinks is good. I haven’t dismissed anything.”

Lincecum, 27, won the 2008 and ’09 National League Cy Young awards and has since committed to a fitness regimen that should improve his chances of long-term success.

The Giants also are trying to reach a new contract agreement with their other premier right-hander, Matt Cain, who is eligible for free agency at the end of next season.

“We’re going to stay engaged with both of them,” Giants assistant general manager Bobby Evans said. “It’s a matter of finding common ground. Our interest in both of them goes beyond this coming season.”

The outcome of the Giants’ negotiations with their two star pitchers almost certainly will influence their pursuits of free agents such as outfielder Carlos Beltran.

The team’s top priority is keeping Lincecum and Cain into the latter part of the decade.

-Ken Rosenthal and Jon Paul Morosi