Wichard said Jason and Katina Taylor likely will return to their home in Weston, Fla., and take the weekend to make a decision.
"This is a guy that I can honestly say the contract is not a motivating factor," Wichard said. "The only things that matter are winning, enjoying football and getting a Super Bowl ring."
Under the terms of the uncapped season, because the Jets made the AFC Championship Game, they had to lose a player to free agency before they could sign one.
The Jets have competition for Taylor's services: Miami wants to re-sign him, and the New England Patriots also are interested.
Jets coach Rex Ryan is interested in Taylor as a means of improving the team's pass rush. Calvin Pace led with eight sacks last season, but the Jets, who had a team sack total of 32, want to add a player with 10-sack potential. The Jets had only 10 combined sacks from their outside linebackers last season.
Taylor, one of the best pass-rushers of his era, has 127½ sacks during his 13-year NFL career. He was on the field for 80 percent of the Dolphins' sacks last season, collecting seven himself.
John Clayton is a senior NFL writer for ESPN.com. ESPN blogger Tim Graham contributed to this report.