Reports claim Rangers are trying to sign former Hibs midfielder on permanent deal
The 22-year-old was previously linked with a move to the Ibrox club last summer but no deal transpired.
Rangers added a number of options in the wide areas this summer, with new boys Sheyi Ojo, Greg Stewart, Jake Hastie and Jordan Jones all capable of playing on the flank.
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Hide AdBut with Daniel Candeias having left and Glenn Middleton expected to depart on loan - possibly to Hibs - Steven Gerrard is still keen on bolstering the area.
Barker impressed during a loan spell at Easter Road in the 2017/18 season, playing 27 times for Neil Lennon's side.