The Ibrox side were one of a number of clubs interested in the 19-year-old this summer, claim the Sunday Mirror.
Foden is regarded as one of England's most talented individuals and recently signed a long-term contract worth £30,000-a-week.
Manchester City manager Pep Guardiola said: "He has everything to become one of the best players. I have said many times in press conferences, but maybe not said it in front of him, Phil is the most, most, most talented player I have ever seen in my career as a manager."
Yet, he has played just ten minutes of first-team football this season in the league with the City boss calling him to be more assertive.
If the club were willing to allow him to leave on loan it is believed Rangers would have faced competition for his signature from Roma.