The 32-year-old started his professional career with the Gers and spent six seasons at the Glasgow club before moving to Blackpool in 2009.
The report claims that Rangers boss Steven Gerrard had pondered over the option of bringing back his former teammate to the Ibrox club in the summer transfer window.
Gerrard played with Adam during the 2011-12 season at Liverpool, and considered signing the Scotland midfielder, who has 32 caps to his name, this summer.