The Lions join the Seattle Seahawks and San Francisco as clubs Hayne has visited since his shock decision to retire from league to pursue an NFL career.
Hayne's American agent, Jack Betcha, has been quoted saying the 26-year-old was impressed by the Lions setup but that "no decision is imminent".
Lions running back Reggie Bush, who met Hayne during a promotional trip to Australia this year, told the Free Press he believed the two-time Dally M Medallist can succeed in the NFL.
"I've seen some of his film, I watched him, and he has all the skill sets that it takes to play in the NFL," Bush said.
The Lions have experience of recruiting from outside the usual avenues.
Last year, they signed up American rugby sevens flyer Carlin Isles to their practice squad and Norwegian Havard Rugland was added to the roster to compete for the kicker's position.
Isles has since returned to rugby, while Rugland lost the kicking job to David Akers.
Whoever Hayne signs for, it's likely he'll be offered a futures deal to enable to him to train with a practice squad and build up his experience.