The Gers are looking to sign Cifuentes and the player, who is out of contract at LAFC at the end of the year, is keen to make the move to Ibrox.
However, agreeing a fee with LAFC is proving to be difficult, with the American club demanding a fee of £1.2m to let him go.
Rangers, who will not pay that much, are confident that LAFC will blink and accept a fee for Cifuentes rather than run the risk of losing him for nothing in six months’ time.
Michael Beale wants the Ecuador international in through the door this summer and the club are trying to make it happen.
Cifuentes has made 17 appearances in the MLS for LAFC so far this season, providing three assists for his team-mates.
Rangers will want the deal done as quickly as possible, with pre-season preparations in full swing.
The Gers are due to play host to Newcastle United in a friendly on 18th July before then hosting German outfit Hamburg on 22nd July and it remains to be seen if Cifuentes is involved in either game.