Rangers have had a new bid worth around £6m accepted for Feyenoord striker Danilo.
The 24-year-old - who scored 12 goals last season - had been the subject of several offers from Rangers, who now look set to seal an eighth summer signing, with the initial fee £5.2m before potential add-ons.
Personal terms are not expected to be an issue, with the Brazilian understood to be keen on a move to Ibrox.
Rangers are also closing in on a summer move for another long-term target - Los Angeles midfielder Jose Cifuentes.
Manager Michael Beale revealed on Sky Sports News on Friday the club had already secured a pre-contract agreement, with his current deal expiring in December.
"It is getting closer. There are logistics with that one and work permits and everything else that goes in between it," he told Sky Sports News about a deal to sign the Ecuador international.
"The clubs are still talking. He's out of contract at the end of the year and we have an agreement for that.
"We would like to bring it to a close early so he can join us in this window.
"Those discussions are ongoing."
Kieran Dowell, Cyriel Dessers, Jack Butland, Sam Lammers, Leon Balogun, Dujon Sterling and Abdallah Sima have already joined Rangers during this transfer window.
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