West was drafted in 2003 by the Hornets, and has averaged 16.4 points and 7.3 rebounds per game during his eight-year career with New Orleans.
The 31-year-old is coming off ACL surgery, but was expected to be among the elite free agents this offseason before the injury.
Celtics coach Doc Rivers seemed to be hinting at another big splash Friday night while talking to reporters about potential moves to complete the team's 2011-12 roster.
Asked if the team was looking for another big or another scorer, Rivers said, "You got it, we're looking for a big scorer. And we are, honestly. But we're just looking for the best players available that are still out there. Some of them are probably a pipe dream. And some may not be, you never know.
"One thing with players, some will just go for the best deal, which you can't blame them for that. Some will go for a fit. Some will just say, 'I'm going to sign for one year, I want to try to win a title.' Those are the ones we're talking to."
ESPNBoston.com's Chris Forsberg contributed to this report.