Johnson told reporters the Jets and a player some have described as the NFL's best defensive performer are "far apart" in the negotiations, The New York Times reported.
Revis has said he wants to be the highest-paid cornerback in football. But it would take $45.3 million over three years to match the reported salary of Oakland's Nnamdi Asomugha -- a figure the Jets have dismissed as unrealistic.
Johnson said the dispute involves the "total compensation" paid to all the Jets players but is not being caused by any unusual circumstances, such as a lack of team cash flow, the newspaper reported.
"This is my 11th year. We've never had an inability because of resources to sign whoever we wanted," he said, adding, "We drafted (Revis). So he's our guy. We love him. We're going to try until we can't anymore."
Notable deaths of 2014 [PHOTOS]