Reiss points out that New England has an open spot on their practice squad.
McGuire, 25, is a former sixth-round pick of the Jets back in 2017. He was in the third year of his four-year, $2.66 million contract when the Jets waived him coming out of the preseason.
The Browns signed McGuire to their practice squad and promoted him last month before being waived and re-signed to their taxi squad. Cleveland cut him loose earlier this week.
In 2018, McGuire appeared in eight games for the Jets and rushed for 276 yards on 92 carries (3 YPC) to go along with 19 receptions for 193 yards receiving and four total touchdowns.