The 31-year-old is being lined up for a potential move as the Gers prepare for their first season back in the Scottish Premiership.
The Record claims that the Gers boss flew out to the USA shortly after the side's friendly win against Tottenham last week to begin talks with the 31-year-old before returning to work on the potential deal that would see the Croatian's former Queens Park Rangers teammate Joey Barton move to the club also.
Kranjcar currently plays for the New York Cosmos but has played over 150 games in the Premier League during spells with Portsmouth, Spurs and finally QPR, and the Record states that Warburton views him as the perfect candidate to play in one of the wide roles as the Light Blues prepare for their first season back in the Scottish Premiership.
The attacking midfielder would surely be an excellent addition if he agreed to a move this summer. His experience at the highest level and on the international stage - he has made 81 appearances for his country during his career - would most likely benefit the younger players in Rangers' squad who have very little knowledge of playing in the top flight.
And with a Scottish Cup final still to play, his previous experience of playing in continental competition may be hugely beneficial if the Gers win against Hibernian and secure a place in the upcoming campaign's Europa League.
Meanwhile, the quality that he would bring to the side immediately would certainly help Warburton's men as they try to challenge for the league title as soon as they get back into the Scottish Premiership.