Talks between Welker and the Patriots haven't been "overly active" in recent days, and "it would be a surprise if an extension was reached," Mike Reiss of ESPN Boston reports.
Welker is already due to come back to the Patriots next season under a $9.5 million franchise tender, but he has been vocal about wanting a contract that includes guaranteed money and at least a couple more years.
Monday at 4 p.m. is the deadline for teams to work out contracts with players who have been placed under the franchise tag for next season.
Welker is coming off of a five-year, $18 million deal with the Patriots, which he signed when he was traded from the Miami Dolphins in 2007. He has since broken several Patriots records and redefined the slot receiver position in the league, accumulating more catches (554) since 2007 than any other receiver.
Welker, 31, has had more than 100 receptions four times with the Patriots. Last year, he racked up 1,569 yards and nine touchdowns on 122 catches as the team went to the Super Bowl for the second time in Welker's tenure with New England.