Neil, who left Sunderland at the end of the season, has been linked with a move to Glasgow.
He had a loan stint at Ipswich Town, helping them to secure promotion, but a permanent move to the Tractor Boys is thought to be unlikely.
This leaves the door open for the 24-year-old to join up with Danny Rohl's squad, who have already brought in Lawrence Shankland from Hearts.
Kyle, who spent a season at Rangers and six years with the Black Cats, has followed Neil's career closely.
He told GO Radio: "I would go regularly to watch Sunderland three, four times a year.
"I remember when Dan Neil broke into the first team, he was the next big thing that the Sunderland fans had expectations for."
Kyle spoke highly of Neil's time at Ipswich, saying: "They got the club through the leagues, was the captain, and then got an opportunity where I don't think he was going to get many games in the Premier League with Sunderland.
"So he took the move to Ipswich and he's done well at Ipswich."
Kyle firmly believes that Neil would be a strong addition to Rangers, saying: "For me, he's a very, very good footballer, and he would be a welcome addition to Rangers.
"I think that Dan Neil would be a great addition to Rangers.
"I've seen him up close, and he's a hardworking, technical, good midfielder."
He also praised Neil's leadership qualities, noting: "He's tenacious in the midfield, gets about, keeps things simple.
"And he was the captain of Sunderland. He took them up through two leagues. So he's well respected."