Durand had faxed six teams a proposal on Tuesday. But, according to The Journal Newspapers, the Redskins made the first counter offer.
''It was worth it enough to keep the dialogue wide open,'' Durand told The Journal Newspapers.
He hopes negotiations can be completed by Friday, but anticipates them lasting until next week.
Mitchell has started most of the past three seasons for the Super Bowl champions, spending time at tackle and end. He was drafted as an end out of Texas A&M.
He's been described as a ''grinder'' and appears to rely more on guts and instinct than raw talent. New England had reportedly wanted to keep him, but felt his price tag was too high. The Patriots instead signed defensive tackle Steve Martin on Wednesday.