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Monday, at the NFL Annual Meeting, Kraft -- donning Patriot-colored Air Force Ones -- said he hopes the sides will come to an agreement.
"He is one of my personal favorites," Kraft said in an interview with reporters in Orlando, Fla. "... I surely hope Vince will be with us next year."
Kraft admitted there still were issues to be worked through to keep the veteran lineman.
"I very much hope we get it done and I believe he very much would like to do it as well," Kraft said. "We'll see what happens."
Wilfork turns 33 in November and is coming off a torn Achilles tendon. He is scheduled to make $7.5 million in 2014, with a salary cap charge of $11.6 million stemming from a five-year contract extension in 2010.
Other comments from Kraft on Monday:
"He had a chance to go to any team, and could've made more money," Kraft said of Revis. "But he chose us."
» Kraft was confident in the background information the team gathered before signing cornerback Brandon Browner.
"Want me to tell Brady that he's at the end of his career?"