Red Sox slugger David Ortiz has gotten pretty adamant about this. He now says that he'll look at walking off after this year, when his current contract runs out, if Boston doesn't give him a two-year deal, presumably to end his career after his age-40 season.
That said, he hasn't hinted at numbers he wants, nor indicated if 1 + a player option (albeit at lower $$ than the guaranteed year) will fit the bill.
If I'm Boston, I don't even begin to think about this until midseason. He is 38. Outside of his more obvious dings in 2008 and 2012, he's not had 550 ABs in a season since 2006, or 150 games played since 2007.
About August, I'd start doing assessing. If it looks like he'll at least end above 2010's statistical line, I'm prepared to cut him a two-year check, likely a full two years. If we're in that "vicinity," but not better, I'm leaning one + player option, with that option year less on cash, but perhaps with some incentives. That's definitely true if he's below his 2008 level.
And, if by mid-August, it looks like Boston has the 2009 Ortiz, he only gets a one-year deal, unless he wants a healthy pay cut as part of this.