The right-back, a member of England’s pool at the FIFA Under-20 World Cup in 2011, recently left Doncaster Rovers after they failed to win promotion to the Sky Bet Championship.
Wabara travelled to Glasgow for talks over the weekend and it is understood he will train with the club at Murray Park this week with a view to signing a contract.
Paul Dickov wanted to keep the 23-year-old, who has previously spent time on loan at Ipswich Town, Blackpool and Oldham Athletic, but Wabara opted to leave and is thought to be keen on a move to Glasgow.
South Africa captain Dean Furman also left Doncaster when the campaign finished and he spent time at Rangers between 2006 and 2008.
He has backed his old team-mate to be a success with the SPFL Championship outfit if he can agree terms and believes he is capable of shining in the English Premier League one day.
Furman said: “I know Reece very well. He’s a very exciting player and Rangers fans would love him. He is very attack-minded and he’s very much in the mould of Dani Alves.
“He’s very quick and loves to get forward. He has lovely ability, loves to beat a man and puts good deliveries into the box. He had quite a few assists last season.
“I can’t speak for the new manager at Rangers but if he’s looking for a young, athletic full-back who can create and join in play, Reece ticks all the right boxes.
“He has been a real pleasure to play with. He has worked extremely hard on his game and is becoming more consistent in his performances.
“Reece did well for Doncaster and has high ambitions. I’m sure he will want to play in the Premier League and I’m sure he can.”
Rangers have already signed two defenders since Warburton took charge at Ibrox a fortnight ago, with Danny Wilson coming in from Hearts and Rob Kiernan signing from Wigan.
The new manager has also held talks with departing Derby midfielder John Eustace while former West Bromwich Albion and Stoke teenager Jordan Gibson has joined the club’s youth squad.