Chris Wesseling of NFL.com reported on Sunday that Welker will do just that for not "paying him what he's worth."
Welker was targeted fewer times than normal early last season, making only 16 receptions through the first three games, which was less than half the number of receptions he'd made at a similar juncture in 2011.
But he still finished with 118 receptions, the third-highest number in his career and only four behind his 2011 total.
So why is Welker apparently making the Patriots pay by testing free agency?
Peter King of Sports Illustrated ranks Welker as the No. 10 available free agent and the No. 3 receiver. Pittsburgh's Mike Wallace and Green Bay's Greg Jennings are ahead of Welker because they are more explosive down the field.
In the first four seasons of Welker's NFL career, he had only 96 catches for 1,121 yards. But in his first with Tom Brady in New England, he had 112 catches and 1,175 receiving yards. Since then, he has exceeded those totals three times and has become Brady's most trusted weapon.
King also reported that Brady received an extension that lessened his contract's impact on the salary cap and would help the team in the short term. So why isn't Welker willing to give the team a discount?
Yes, Brady has already earned much more than Welker in his career. But now Welker looks like the bad guy for appearing to value money more than winning.
The Patriots have made it to two Super Bowls in the last six years, losing to the New York Giants each time. They fell to the Baltimore Ravens in last season's AFC title game, so they have what it takes to contend every year.
If Welker wants to "stick it" to the Patriots and take more money from another team, he has earned the right to do so. With 672 catches since joining the Patriots in 2007, he has the most catches in the NFL over that span.
NFL.com's Bucky Brooks argues that Welker is a product of the New England system. Granted, it was at the beginning of his career, but Welker didn't prove that he could be a great player in a different system.
Only since joining Brady and being part of a receiving corps that has included Julian Edelman, Deion Branch and, more recently, tight ends Rob Gronkowski and Aaron Hernandez has Welker turned into the top slot receiver in football.
Were Welker to re-sign with the Patriots, he figures to continue to make more than 100 receptions.
The 31-year-old has the talent and the hands to succeed anywhere, but there's not a better system for him than the one in New England. It gives him a chance to win and put up mind-blowing numbers.
While he deserves to get paid, he should be willing to put aside any past issues that he has had with the organization. Welker has been a mainstay in the league's best offense for years now, and it would be a mistake for him to throw it all away just to get back at a coach.
*All stats are from NFL.com.