The Jets are dealing with a number of injuries at receiver, which led to them signing Rishard Matthews on Tuesday.
Butler, 28, is a former seventh-round pick of the Raiders back in 2013. He spent two years in Oakland before he was traded to the Cowboys for the 2015 season.
The Cowboys re-signed Butler to a one-year contract last year and he finished out the season in Dallas. Butler joined the Cardinals back in April on a two-year contract, but was cut loose coming out of the preseason.
Butler returned to the Cowboys for a brief stint earlier this season.
In 2017, Butler appeared in 13 games for the Cowboys and caught 15 passes for 317 yards receiving and three touchdowns.
We have him featured in our Top 50 Available 2018 NFL Free Agents list.