On Tuesday, TMZ Sports reported Gordon is training alongside Montgomery six times a week at the NUMA Speed facility in Gainesville, Florida.
Gordon, who was suspended for violating the terms of his reinstatement under the league's substance abuse policy, released a statement shortly before the latest ban was announced saying he'd be leaving the Patriots to focus on his mental health.
"I take my mental health very seriously at this point to ensure I remain able to perform at the highest level. I have recently felt like I could have a better grasp on things mentally. With that said, I will be stepping away from the football field for a bit to focus on my mental health," Gordon said.
The 2013 All-Pro selection recorded 40 catches for 720 yards and three touchdowns in 11 appearances for New England before the suspension.
Meanwhile, Montgomery helped the United States win gold in the 4x100-meter relay at the 2000 Summer Olympics in Sydney, Australia.
In 2013, Montgomery told Rachel Axon of USA Today he was a changed man: "There's nothing else I want. I had everything else—fast cars, had money, had clothes, had jewelry, traveled the world. I still ended up at the bottom."
The NFL hasn't provided a timetable for Gordon's potential reinstatement after he missed the Patriots' run to the Super Bowl LIII title.