And then the trade winds blew in another direction.
Before long, the news officially came out. Not only wasn't it Boston, but Frazier wound up with the rival Yankees and was traded to the Bronx along with impact reliever David Robertson as part of a seven-player deal.
"Two players, two pretty good players," Red Sox first baseman Hanley Ramirez said fresh off of a walk-off homer in the 15th inning to beat the Blue Jays, 5-4. "But I believe in our team. We'll just see. We have to keep pushing to the limit."
The American League East is heating up with less than two weeks left before the July 31 non-waiver Trade Deadline. Red Sox president of baseball operations Dave Dombrowski has never been shy about making moves in July, so all eyes will be on what he does to counter the move by New York.
In particular, there is interest in what kind of bat the Red Sox can get. The offense has struggled to score coming out of the All-Star break and is last in the AL with 97 homers.
Though Frazier, who belted 40 homers last year and has 16 this season, was arguably the biggest bopper of the third basemen on the market, there are still some productive players Boston might be able to get.
Jed Lowrie becomes a top name to keep an eye on. The switch-hitting Lowrie (10 homers, .780 OPS) is having a solid season for the Athletics and is quite familiar with the Red Sox, having played his first four seasons in Boston. A's executive vice president of baseball operations Billy Beane is always looking to make deals this time of year.
If Lowrie went back to Boston, the Red Sox would be the third team he's had two stints with. Lowrie has been a two-time Astro and Athletic.
The Angels' Yunel Escobar (.284/.343/.408) is another AL West player who could be dangled in a trade. The Red Sox will get a better look at him this weekend when they travel to Anaheim for a three-game series.
The Pirates will listen to what teams have to offer for David Freese and All-Star Josh Harrison. The Giants could move on from Eduardo Nunez.
The only hope in getting All-Star Mike Moustakas from the Royals at this point is if Kansas City goes into a free-fall over the next couple of weeks.
If Dombrowski can't find the fit he is looking for on the trade market, he could always promote his top prospect to the Major Leagues in third baseman Rafael Devers, who had a sparkling debut last week at Triple-A Pawtucket.
Remember that last year, when Dombrowski didn't get his top trade target in left field in Carlos Beltran, he went to the farm system and brought up Andrew Benintendi. That obviously worked out well.
With a two-game lead in the AL East, the Red Sox will leave the wheeling and dealing to Dombrowski.
"Honestly, me personally, I can't really focus on that," said Red Sox center fielder Jackie Bradley Jr. "I just try to focus on playing and helping the team. Obviously there are rumors for a reason and there are always going to be rumors until something comes to fruition."