The Ibrox club were initially a 16/1 outsider of landing the forward before their chances fell to 6/4 last night, according to Sky Bet.
Since then other bookmakers have slashed their odds significantly with Ladbrokes, who sponsor the SPFL, going as far as to suspend betting after a flurry of activity on the market.
David Macdonald of Ladbrokes said: “The money is down for van Persie to join Rangers and we’ve been left with no choice but to take a breather. Clearly plenty of Gers fans expect some exciting news sooner rather than later.”
Van Persie previously revealed his desire to join Rangers as a teenager when he was still with Feyenoord.
The Dutch international had been told of interest from Ibrox and he “sat by the phone” for a call that never came.
He told The Independent in 2009: “There was some interest from Rangers when I was at Feyenoord.
“The problem for me was they didn’t come in and make an offer. I was quite interested because I really wanted to leave my club.
“Rangers are massive. My European debut was against Rangers at Ibrox and that was a fantastic moment. When I heard about their interest, I sat by the phone hoping it would ring.
“I was in a difficult situation at my club and desperate to leave. Advocaat told me he needed to sell some players before he could buy. That’s why it dragged on and did not happen.”
Van Persie is currently at Turkish side Fenerbahce. He joined on a three-year deal from Manchester United for a fee of £3.84 million last summer.