While the 32-year-old Victorino has been a center fielder for most of his career, he would likely shift to right field for the Red Sox, at least for 2013.
Jacoby Ellsbury is under contract with Boston for one more season.
"In our ballpark, we'd like to have someone who's played a lot of center in right field -- if we can," Cherington said. "There's guys out there that have done both. If you play a lot of center field and play in different parks, there may be a little bit of an adjustment, but he can figure out right field at Fenway."
Boston's offer to Victorino was first reported by The Boston Globe.
With Fenway Park's cavernous right field, the Red Sox always prefer to have a strong defender in that spot.
That is clearly Victorino, a two-time All-Star and three-time Gold Glove Award winner who has spent most of his career with the Phillies.
"It's probably the toughest right field in baseball to play, just in terms of the space to cover," said manager John Farrell, "so that range comes into play. It might not be your prototypical right fielder where it's a power bat, because we do value the defense in that area. That's not to exclude anyone, but defense takes a high priority, in that position at Fenway particularly."
The Indians were another team that was pushing hard for Victorino.
Last week, Boston signed Jonny Gomes. With Victorino coming on board, that would likely rule out any chance of bringing free agent Cody Ross back. In 2012, Ross was one of the few bright spots for the Red Sox. He was seeking a deal worth roughly $25 million over three years.
"Obviously I don't want to say too much about the specific nature of the conversations because they go back a ways," Cherington said. "As of now we haven't been able to find something that makes sense, but the door is still open and we'll see what else happens. Again, he has other options, too."
When the season ended, Cherington said that the club wanted to retain David Ortiz and Ross. They were successful with Ortiz.
"We talked during the season and right after the season, and we've talked since then," Cherington said. "But we obviously weren't able to reach an agreement early in the process. Once we got into free agency we kept the dialogue open, but it just hasn't culminated in anything yet."
The Red Sox have Ellsbury, Gomes and Victorino slated to play key roles in the outfield in 2013, with depth alternatives like Daniel Nava and Ryan Kalish also available.
However, Cherington will still be active in the outfield market.
"We know we want to add to the outfield," said Cherington. "We're working on that and hopefully making some progress. I'd just say that we wouldn't necessarily stop with one addition, but we don't feel like it's essential."
If the Red Sox do add another outfielder, the preference would be for a left-handed hitter.
"Obviously, we're probably a little more right-handed right now than in some years past. Ideally we would like to create some more balance, but we'll see," said Cherington.
A switch-hitter, Victorino is a career .275 hitter with 90 homers, 409 RBIs and 201 stolen bases in 1,076 career games.
He has been better from the right side, hitting .301 with 40 homers, 127 RBIs and an .881 OPS in 1,080 at-bats. As a left-handed hitter, Victorino is a .265 hitter with 50 homers, 282 RBIs and a .727 OPS over 2,772 at-bats.
Victorino's 2012 season was a down one offensively, as he hit .255 with 11 homers and 55 RBIs, splitting the year between the Phillies and Dodgers. Victorino stole 39 bases, which would give the Sox an element of speed they don't have much of beyond Ellsbury.
Now that the Sox are physicals away from signing their slugger (Napoli) and right fielder (Victorino), the next need Cherington would like to fill is a starting pitcher.
You can cross one name off the list. Dan Haren agreed to terms on a one-year, $13 million deal with the Nationals on Tuesday.
Brandon McCarthy could be a good fit for the Red Sox.
"It seems a little slower to develop," Cherington said of the starting pitching market. "Obviously someone like Haren went off the board. We'll see if that shakes it loose at all."