The six-year veteran said he hoped the team would use the tag for that purpose.
The Patriots placed a non-exclusive tag on Wilfork, according to ESPN.com. That gives the Patriots the right to match any other team's offer or let Wilfork go for two first-round draft picks. An exclusive tag would have tied Wilfork to the Patriots for the season.
As a non-exclusive franchise player, if a long-term deal is not reached, his 2011 salary with the Patriots would be $7 million, the average 2009 salary of the top five paid players at his position.
"A long-term agreement with Vince Wilfork has been the team's top contractual priority for some time," the Patriots said in a statement. "Unfortunately, despite numerous conversations and proposals, the goal has not yet been realized. Vince is a tremendous player for our team and remains a significant part of our future plans."
The Patriots also said, "We are hopeful that Vince will remain a Patriot for many years to come."
Last month, Wilfork said on WEEI radio in Boston that the franchise tag would be a "slap in the face."
But he struck a more accommodating tone on Monday in a posting to the Twitter account of his wife Bianca.
"After six years of dedicated service I do understand this is a business," it said. "With that being said it is my hope that the tag is applied for its true purpose. For the purpose of allotting more time for us to continue our talks and be able to reach a long term agreement. Only time will tell what the final result will be."
The Patriots noted that in 2002, they named kicker Adam Vinatieri a franchise player then reached agreement on a three-year contract extension. They used it again on Vinatieri in 2005 and cornerback Asante Samuel in 2007 and both left as free agents after those seasons.
The team had a deadline of Thursday for putting the tag on Wilfork.