The Gers have identified Cifuentes as a priority signing and boss Michael Beale wants the Ecuador international at Ibrox to beef up his squad.
Cifuentes’ agent has been to Scotland to speak to the Gers and it is suggested that personal terms should not be an issue.
However, Rangers are waiting until 1st July, when they can officially offer Cifuentes a pre-contractual agreement.
Cifuentes is out of contract at LAFC at the end of the year and from July would be free to sign a deal with the Gers.
LAFC can demand a substantial fee to let Cifuentes go now, but once the player pens a contract with Rangers, the Gers could look to lower the price and bring him over this summer.
Cifuentes has made 12 appearances in the MLS for LAFC so far this season, picking up two bookings along the way.
The 15-cap Ecuador star provided an assist in the Los Angeles derby against LA Galaxy in April, as LAFC won 3-2.