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.
However, Rangers cooled their interest in the Stoke City midfielder following the arrivals of Scott Arfield, Lassana Coulibaly and Ovie Ejaria at the Ibrox club.
Change in strategy – smart decision from Gerrard
Although Adam would have added experience in the middle of the park, the signing would have been hardly inspiring. Clearly, Adam is on the decline, and it would have made no sense to shoe-horn a player who is on high wages into an ill-fitting system.
On the other hand, the young players have added energy and dynamism in the middle of the park. The players brought in are far from household names, but they have added spark in the team, and the results are clearly evident.
Rangers have taken a sea-change route to their transfer dealings under Gerrard, and turning to younger players by snubbing a veteran midfielder is testimony of that approach.